<p>Considere uma distribuição binomial para o caminho aleatório em uma dimensão com <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“7.487ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 3223.6 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title” data-mathml="undefined">
<title> N = 15</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”/>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”/>
<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”/>
<path stroke-width=“1” id=“E1-MJMAIN-35” d=“M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z”/>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-4E" x=“0” y=“0”/>
<use xlink:href="#E1-MJMAIN-3D" x=“1166” y=“0”/>
<g transform=“translate(2222,0)”>
<use xlink:href="#E1-MJMAIN-31"/>
<use xlink:href="#E1-MJMAIN-35" x=“500” y=“0”/>
</g>
</g>
</svg>. Há modificações sensíveis?</p>

Passo 1

<p>E aí, galerinha!</p>
<p>Temos um caminho aleatório unidimensional modelado por uma distribuição binomial com <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“7.487ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 3223.6 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> N = 60</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-36” d=“M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-30” d=“M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-4E" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1166” y=“0”></use>
<g transform=“translate(2222,0)”>
<use xlink:href="#E1-MJMAIN-36"></use>
<use xlink:href="#E1-MJMAIN-30" x=“500” y=“0”></use>
</g>
</g>
</svg> passos, probabilidade de passo à direita <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“7.845ex” height=“2.843ex” style=“vertical-align: -0.838ex; margin-left: -0.089ex;” viewBox="-38.5 -863.1 3377.6 1223.9" role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> p = 2 / 3</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-70” d=“M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-32” d=“M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2F” d=“M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-33” d=“M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-70" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-3D" x=“781” y=“0”></use>
<use xlink:href="#E1-MJMAIN-32" x=“1837” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2F" x=“2338” y=“0”></use>
<use xlink:href="#E1-MJMAIN-33" x=“2838” y=“0”></use>
</g>
</svg> e à esquerda <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“7.655ex” height=“2.843ex” style=“vertical-align: -0.838ex;” viewBox=“0 -863.1 3296.1 1223.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> q = 1 / 3</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-71” d=“M33 157Q33 258 109 349T280 441Q340 441 372 389Q373 390 377 395T388 406T404 418Q438 442 450 442Q454 442 457 439T460 434Q460 425 391 149Q320 -135 320 -139Q320 -147 365 -148H390Q396 -156 396 -157T393 -175Q389 -188 383 -194H370Q339 -192 262 -192Q234 -192 211 -192T174 -192T157 -193Q143 -193 143 -185Q143 -182 145 -170Q149 -154 152 -151T172 -148Q220 -148 230 -141Q238 -136 258 -53T279 32Q279 33 272 29Q224 -10 172 -10Q117 -10 75 30T33 157ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2F” d=“M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-33” d=“M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-71" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-3D" x=“738” y=“0”></use>
<use xlink:href="#E1-MJMAIN-31" x=“1794” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2F" x=“2295” y=“0”></use>
<use xlink:href="#E1-MJMAIN-33" x=“2795” y=“0”></use>
</g>
</svg>.Seja <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.92ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 1257.4 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> N 1 </title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-4E" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-31" x=“1136” y="-213"></use>
</g>
</svg> = número de passos à direita (então posição final = <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“27.48ex” height=“2.843ex” style=“vertical-align: -0.838ex;” viewBox=“0 -863.1 11831.6 1223.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> N 1 - ( N - N 1 ) = 2 N 1 - N</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2212” d=“M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-28” d=“M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-29” d=“M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-32” d=“M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-4E" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-31" x=“1136” y="-213"></use>
<use xlink:href="#E1-MJMAIN-2212" x=“1479” y=“0”></use>
<use xlink:href="#E1-MJMAIN-28" x=“2480” y=“0”></use>
<use xlink:href="#E1-MJMATHI-4E" x=“2869” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2212" x=“3980” y=“0”></use>
<g transform=“translate(4981,0)”>
<use xlink:href="#E1-MJMATHI-4E" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-31" x=“1136” y="-213"></use>
</g>
<use xlink:href="#E1-MJMAIN-29" x=“6238” y=“0”></use>
<use xlink:href="#E1-MJMAIN-3D" x=“6905” y=“0”></use>
<use xlink:href="#E1-MJMAIN-32" x=“7962” y=“0”></use>
<g transform=“translate(8462,0)”>
<use xlink:href="#E1-MJMATHI-4E" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-31" x=“1136” y="-213"></use>
</g>
<use xlink:href="#E1-MJMAIN-2212" x=“9942” y=“0”></use>
<use xlink:href="#E1-MJMATHI-4E" x=“10943” y=“0”></use>
</g>
</svg>).</p>
<p>Pedem-se:(a) Traçar o gráfico da probabilidade binomial <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“7.913ex” height=“2.843ex” style=“vertical-align: -0.838ex;” viewBox=“0 -863.1 3407.2 1223.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> P N ( N 1 )</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-50” d=“M287 628Q287 635 230 637Q206 637 199 638T192 648Q192 649 194 659Q200 679 203 681T397 683Q587 682 600 680Q664 669 707 631T751 530Q751 453 685 389Q616 321 507 303Q500 302 402 301H307L277 182Q247 66 247 59Q247 55 248 54T255 50T272 48T305 46H336Q342 37 342 35Q342 19 335 5Q330 0 319 0Q316 0 282 1T182 2Q120 2 87 2T51 1Q33 1 33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM645 554Q645 567 643 575T634 597T609 619T560 635Q553 636 480 637Q463 637 445 637T416 636T404 636Q391 635 386 627Q384 621 367 550T332 412T314 344Q314 342 395 342H407H430Q542 342 590 392Q617 419 631 471T645 554Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-28” d=“M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-29” d=“M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-50" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-4E" x=“908” y="-213"></use>
<use xlink:href="#E1-MJMAIN-28" x=“1370” y=“0”></use>
<g transform=“translate(1760,0)”>
<use xlink:href="#E1-MJMATHI-4E" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-31" x=“1136” y="-213"></use>
</g>
<use xlink:href="#E1-MJMAIN-29" x=“3017” y=“0”></use>
</g>
</svg> versus <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“6.147ex” height=“2.843ex” style=“vertical-align: -0.838ex;” viewBox=“0 -863.1 2646.4 1223.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> N 1 / N</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2F” d=“M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-4E" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-31" x=“1136” y="-213"></use>
<use xlink:href="#E1-MJMAIN-2F" x=“1257” y=“0”></use>
<use xlink:href="#E1-MJMATHI-4E" x=“1757” y=“0”></use>
</g>
</svg> (fração de passos à direita).(b) Obter a distribuição gaussiana (aproximação normal) correspondente <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“6.309ex” height=“2.843ex” style=“vertical-align: -0.838ex;” viewBox=“0 -863.1 2716.5 1223.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> P c ( N )</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-50” d=“M287 628Q287 635 230 637Q206 637 199 638T192 648Q192 649 194 659Q200 679 203 681T397 683Q587 682 600 680Q664 669 707 631T751 530Q751 453 685 389Q616 321 507 303Q500 302 402 301H307L277 182Q247 66 247 59Q247 55 248 54T255 50T272 48T305 46H336Q342 37 342 35Q342 19 335 5Q330 0 319 0Q316 0 282 1T182 2Q120 2 87 2T51 1Q33 1 33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM645 554Q645 567 643 575T634 597T609 619T560 635Q553 636 480 637Q463 637 445 637T416 636T404 636Q391 635 386 627Q384 621 367 550T332 412T314 344Q314 342 395 342H407H430Q542 342 590 392Q617 419 631 471T645 554Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-63” d=“M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-28” d=“M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-29” d=“M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-50" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMATHI-63" x=“908” y="-213"></use>
<use xlink:href="#E1-MJMAIN-28" x=“1049” y=“0”></use>
<use xlink:href="#E1-MJMATHI-4E" x=“1438” y=“0”></use>
<use xlink:href="#E1-MJMAIN-29" x=“2327” y=“0”></use>
</g>
</svg> com mesma média e variância da binomial e traçar no mesmo tipo de gráfico, comparando com (a).(c) Repetir para <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“7.487ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 3223.6 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> N = 30</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-33” d=“M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-30” d=“M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-4E" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1166” y=“0”></use>
<g transform=“translate(2222,0)”>
<use xlink:href="#E1-MJMAIN-33"></use>
<use xlink:href="#E1-MJMAIN-30" x=“500” y=“0”></use>
</g>
</g>
</svg> e <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“7.487ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 3223.6 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> N = 15</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-35” d=“M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-4E" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1166” y=“0”></use>
<g transform=“translate(2222,0)”>
<use xlink:href="#E1-MJMAIN-31"></use>
<use xlink:href="#E1-MJMAIN-35" x=“500” y=“0”></use>
</g>
</g>
</svg> e verificar se há mudanças sensíveis na aproximação.</p>
<p><b>Como vamos resolver isso?</b></p>
<p>A distribuição binomial é:</p>
<p style=“text-align:center;”><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“46.544ex” height=“6.176ex” style=“vertical-align: -2.505ex;” viewBox=“0 -1580.7 20039.9 2659.1” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> P N ( N 1 ) = N N 1 p N 1 q N - N 1 , N 1 = 0,1 , … , N .</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-50” d=“M287 628Q287 635 230 637Q206 637 199 638T192 648Q192 649 194 659Q200 679 203 681T397 683Q587 682 600 680Q664 669 707 631T751 530Q751 453 685 389Q616 321 507 303Q500 302 402 301H307L277 182Q247 66 247 59Q247 55 248 54T255 50T272 48T305 46H336Q342 37 342 35Q342 19 335 5Q330 0 319 0Q316 0 282 1T182 2Q120 2 87 2T51 1Q33 1 33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM645 554Q645 567 643 575T634 597T609 619T560 635Q553 636 480 637Q463 637 445 637T416 636T404 636Q391 635 386 627Q384 621 367 550T332 412T314 344Q314 342 395 342H407H430Q542 342 590 392Q617 419 631 471T645 554Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-28” d=“M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-29” d=“M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z”></path>
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<path stroke-width=“1” id=“E1-MJSZ3-28” d=“M701 -940Q701 -943 695 -949H664Q662 -947 636 -922T591 -879T537 -818T475 -737T412 -636T350 -511T295 -362T250 -186T221 17T209 251Q209 962 573 1361Q596 1386 616 1405T649 1437T664 1450H695Q701 1444 701 1441Q701 1436 681 1415T629 1356T557 1261T476 1118T400 927T340 675T308 359Q306 321 306 250Q306 -139 400 -430T690 -924Q701 -936 701 -940Z”></path>
<path stroke-width=“1” id=“E1-MJSZ3-29” d=“M34 1438Q34 1446 37 1448T50 1450H56H71Q73 1448 99 1423T144 1380T198 1319T260 1238T323 1137T385 1013T440 864T485 688T514 485T526 251Q526 134 519 53Q472 -519 162 -860Q139 -885 119 -904T86 -936T71 -949H56Q43 -949 39 -947T34 -937Q88 -883 140 -813Q428 -430 428 251Q428 453 402 628T338 922T245 1146T145 1309T46 1425Q44 1427 42 1429T39 1433T36 1436L34 1438Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-70” d=“M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z”></path>
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<g transform=“translate(12772,0)”>
<use xlink:href="#E1-MJMATHI-4E" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-31" x=“1136” y="-213"></use>
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<use xlink:href="#E1-MJMAIN-3D" x=“14307” y=“0”></use>
<g transform=“translate(15363,0)”>
<use xlink:href="#E1-MJMAIN-30"></use>
<use xlink:href="#E1-MJMAIN-2C" x=“500” y=“0”></use>
<use xlink:href="#E1-MJMAIN-31" x=“779” y=“0”></use>
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<use xlink:href="#E1-MJMAIN-2C" x=“16643” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2026" x=“17088” y=“0”></use>
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</svg></p>
<p>Média: <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“11.061ex” height=“2.843ex” style=“vertical-align: -0.838ex;” viewBox=“0 -863.1 4762.5 1223.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> ⟨ N 1 ⟩ = N p</title>
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<use xlink:href="#E1-MJMAIN-27E9" x=“1646” y=“0”></use>
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</svg>, variância: <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“9.786ex” height=“2.843ex” style=“vertical-align: -0.671ex;” viewBox=“0 -934.9 4213.3 1223.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> σ 2 = N p q</title>
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<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-32" x=“810” y=“513”></use>
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</svg>.A aproximação gaussiana para grandes <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.064ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 888.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> N</title>
<defs aria-hidden=“true”>
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</svg> (com correção de continuidade se necessário) é:</p>
<p style=“text-align:center;”><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“42.458ex” height=“10.176ex” style=“vertical-align: -4.505ex;” viewBox=“0 -2441.8 18280.5 4381.3” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> P c ( N 1 ) ≈ 1 2 π σ 2 exp ⁡ - N 1 N p ) 2 2 σ 2 .</title>
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<p>Como queremos comparar visualmente, podemos plotar os pontos discretos da binomial e a curva contínua da gaussiana em função de <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“10.575ex” height=“2.843ex” style=“vertical-align: -0.838ex;” viewBox=“0 -863.1 4553 1223.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> x = N 1 / N</title>
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</svg>.</p>
<p>Para <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.064ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 888.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> N</title>
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</svg> menor, a aproximação deve piorar, especialmente nas caudas e se <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.259ex” height=“2.009ex” style=“vertical-align: -0.671ex; margin-left: -0.089ex;” viewBox="-38.5 -576.1 542 865.1" role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> p</title>
<defs aria-hidden=“true”>
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</svg> não for próximo de 0,5 (aqui <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“7.845ex” height=“2.843ex” style=“vertical-align: -0.838ex; margin-left: -0.089ex;” viewBox="-38.5 -863.1 3377.6 1223.9" role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> p = 2 / 3</title>
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<path stroke-width=“1” id=“E1-MJMATHI-70” d=“M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z”></path>
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<path stroke-width=“1” id=“E1-MJMAIN-32” d=“M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2F” d=“M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-33” d=“M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-70" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-3D" x=“781” y=“0”></use>
<use xlink:href="#E1-MJMAIN-32" x=“1837” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2F" x=“2338” y=“0”></use>
<use xlink:href="#E1-MJMAIN-33" x=“2838” y=“0”></use>
</g>
</svg>, então há assimetria). A aproximação normal ainda é razoável se <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“3.233ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 1392 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> N p</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-70” d=“M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-4E" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMATHI-70" x=“888” y=“0”></use>
</g>
</svg> e <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“3.133ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 1349 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> N q</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-71” d=“M33 157Q33 258 109 349T280 441Q340 441 372 389Q373 390 377 395T388 406T404 418Q438 442 450 442Q454 442 457 439T460 434Q460 425 391 149Q320 -135 320 -139Q320 -147 365 -148H390Q396 -156 396 -157T393 -175Q389 -188 383 -194H370Q339 -192 262 -192Q234 -192 211 -192T174 -192T157 -193Q143 -193 143 -185Q143 -182 145 -170Q149 -154 152 -151T172 -148Q220 -148 230 -141Q238 -136 258 -53T279 32Q279 33 272 29Q224 -10 172 -10Q117 -10 75 30T33 157ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-4E" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMATHI-71" x=“888” y=“0”></use>
</g>
</svg> forem ≥ 5, mas vamos verificar.</p>
<p>Vamos fazer numericamente/graficamente de forma descritiva, já que não podemos traçar gráficos reais aqui, mas descreveremos os resultados qualitativos.</p>

Passo 2

<p><b>Parâmetros fixos:</b> <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“7.845ex” height=“2.843ex” style=“vertical-align: -0.838ex; margin-left: -0.089ex;” viewBox="-38.5 -863.1 3377.6 1223.9" role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> p = 2 / 3</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-70” d=“M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-32” d=“M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2F” d=“M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-33” d=“M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-70" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-3D" x=“781” y=“0”></use>
<use xlink:href="#E1-MJMAIN-32" x=“1837” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2F" x=“2338” y=“0”></use>
<use xlink:href="#E1-MJMAIN-33" x=“2838” y=“0”></use>
</g>
</svg>, <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“7.655ex” height=“2.843ex” style=“vertical-align: -0.838ex;” viewBox=“0 -863.1 3296.1 1223.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> q = 1 / 3</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-71” d=“M33 157Q33 258 109 349T280 441Q340 441 372 389Q373 390 377 395T388 406T404 418Q438 442 450 442Q454 442 457 439T460 434Q460 425 391 149Q320 -135 320 -139Q320 -147 365 -148H390Q396 -156 396 -157T393 -175Q389 -188 383 -194H370Q339 -192 262 -192Q234 -192 211 -192T174 -192T157 -193Q143 -193 143 -185Q143 -182 145 -170Q149 -154 152 -151T172 -148Q220 -148 230 -141Q238 -136 258 -53T279 32Q279 33 272 29Q224 -10 172 -10Q117 -10 75 30T33 157ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2F” d=“M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-33” d=“M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-71" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-3D" x=“738” y=“0”></use>
<use xlink:href="#E1-MJMAIN-31" x=“1794” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2F" x=“2295” y=“0”></use>
<use xlink:href="#E1-MJMAIN-33" x=“2795” y=“0”></use>
</g>
</svg>.</p>
<p><b>(a) e (b) para </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“7.81ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 3362.6 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> N = 60</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-4E” d=“M258 624H235Q214 624 209 626T199 639Q203 678 216 684Q220 686 344 686H434Q464 686 477 680Q480 677 607 454Q738 227 739 227Q742 227 789 418T836 618Q836 620 835 620L821 622Q811 622 779 624Q755 624 749 625T740 632Q737 635 737 644Q737 656 742 669T754 685Q755 685 757 685T763 686Q768 686 803 685T890 684Q925 684 951 684T990 685T1006 686Q1014 686 1016 684Q1027 679 1027 668Q1023 632 1011 626Q1007 624 978 624Q912 622 907 617Q907 616 831 314T753 8Q749 0 723 0H712Q699 0 692 7Q692 8 671 44T607 155T526 296L361 580L296 323Q234 74 234 68T302 62H307Q334 62 334 44Q330 6 317 2L313 0L280 1Q260 2 181 2Q125 2 96 1T63 0Q48 0 43 15Q43 19 47 35Q52 55 57 58T94 62Q147 64 164 69L233 345Q302 619 302 622Q302 624 258 624Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-36” d=“M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-30” d=“M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-4E" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1305” y=“0”></use>
<g transform=“translate(2361,0)”>
<use xlink:href="#E1-MJMAIN-36"></use>
<use xlink:href="#E1-MJMAIN-30" x=“500” y=“0”></use>
</g>
</g>
</svg><b>:</b></p>
<ul>
<li>Média: <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“24.908ex” height=“2.843ex” style=“vertical-align: -0.838ex;” viewBox=“0 -863.1 10724.1 1223.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> μ = N p = 60 × 2 / 3 = 40</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-3BC” d=“M58 -216Q44 -216 34 -208T23 -186Q23 -176 96 116T173 414Q186 442 219 442Q231 441 239 435T249 423T251 413Q251 401 220 279T187 142Q185 131 185 107V99Q185 26 252 26Q261 26 270 27T287 31T302 38T315 45T327 55T338 65T348 77T356 88T365 100L372 110L408 253Q444 395 448 404Q461 431 491 431Q504 431 512 424T523 412T525 402L449 84Q448 79 448 68Q448 43 455 35T476 26Q485 27 496 35Q517 55 537 131Q543 151 547 152Q549 153 557 153H561Q580 153 580 144Q580 138 575 117T555 63T523 13Q510 0 491 -8Q483 -10 467 -10Q446 -10 429 -4T402 11T385 29T376 44T374 51L368 45Q362 39 350 30T324 12T288 -4T246 -11Q199 -11 153 12L129 -85Q108 -167 104 -180T92 -202Q76 -216 58 -216Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
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</svg>.</li>
<li>Variância: <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“62.344ex” height=“3.176ex” style=“vertical-align: -1.005ex;” viewBox=“0 -934.9 26842.4 1367.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> σ 2 = N p q = 60 × ( 2 / 3 ) × ( 1 / 3 ) = 60 × 2 / 9 = 120 / 9 ≈ 13.333</title>
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</svg>, então <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“9.725ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 4187.1 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> σ ≈ 3.651</title>
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<p><b>Binomial:</b></p>
<p style=“text-align:center;”><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“38.498ex” height=“7.509ex” style=“vertical-align: -3.171ex;” viewBox=“0 -1867.7 16575.6 3233.2” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> P 60 ( N 1 ) = 60 N 1 2 3 N 1 1 3 60 - N 1 .</title>
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</svg></p>
<p>Valores significativos estão em torno de <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“8.344ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 3592.5 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> N 1 = 40</title>
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<use xlink:href="#E1-MJMAIN-30" x=“500” y=“0”></use>
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</g>
</svg>.Plotamos <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“8.098ex” height=“2.843ex” style=“vertical-align: -0.838ex;” viewBox=“0 -863.1 3486.7 1223.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> P 60 ( N 1 )</title>
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</svg> vs <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“6.408ex” height=“2.843ex” style=“vertical-align: -0.838ex;” viewBox=“0 -863.1 2758.9 1223.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> N 1 / 60</title>
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</svg> (de 0 a 1).</p>
<p><b>Gaussiana:</b></p>
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<title> P c ( N 1 ) = 1 2 π ⋅ 13.333 exp ⁡ - N 1 40 ) 2 2 ⋅ 13.333 .</title>
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<use xlink:href="#E1-MJMAIN-22C5" x=“722” y=“0”></use>
<g transform=“translate(1223,0)”>
<use xlink:href="#E1-MJMAIN-31"></use>
<use xlink:href="#E1-MJMAIN-33" x=“500” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2E" x=“1001” y=“0”></use>
<use xlink:href="#E1-MJMAIN-33" x=“1279” y=“0”></use>
<use xlink:href="#E1-MJMAIN-33" x=“1780” y=“0”></use>
<use xlink:href="#E1-MJMAIN-33" x=“2280” y=“0”></use>
</g>
</g>
</g>
</g>
</g>
<g transform=“translate(6728,2320)”>
<use xlink:href="#E1-MJSZ4-23A4" x=“0” y="-1155"></use>
<g transform=“translate(0,-2388.737392384106) scale(1,1.05760761589404)”>
<use xlink:href="#E1-MJSZ4-23A5"></use>
</g>
<use xlink:href="#E1-MJSZ4-23A6" x=“0” y="-3496"></use>
</g>
</g>
</g>
<use xlink:href="#E1-MJMAIN-2E" x=“20088” y=“0”></use>
</g>
</svg></p>
<p>Plotamos a mesma curva contínua em função de <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“6.408ex” height=“2.843ex” style=“vertical-align: -0.838ex;” viewBox=“0 -863.1 2758.9 1223.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> N 1 / 60</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2F” d=“M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-36” d=“M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-30” d=“M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-4E" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-31" x=“1136” y="-213"></use>
<use xlink:href="#E1-MJMAIN-2F" x=“1257” y=“0”></use>
<g transform=“translate(1757,0)”>
<use xlink:href="#E1-MJMAIN-36"></use>
<use xlink:href="#E1-MJMAIN-30" x=“500” y=“0”></use>
</g>
</g>
</svg>.</p>
<p><b>Comparação:</b> Para <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“7.487ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 3223.6 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> N = 60</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-36” d=“M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-30” d=“M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-4E" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1166” y=“0”></use>
<g transform=“translate(2222,0)”>
<use xlink:href="#E1-MJMAIN-36"></use>
<use xlink:href="#E1-MJMAIN-30" x=“500” y=“0”></use>
</g>
</g>
</svg>, a gaussiana se ajusta muito bem à binomial, exceto talvez nas extremidades (caudas) onde a binomial é discreta e a gaussiana atribui probabilidade não nula a valores impossíveis (e.g., <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“7.181ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 3092 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> N 1 < 0</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3C” d=“M694 -11T694 -19T688 -33T678 -40Q671 -40 524 29T234 166L90 235Q83 240 83 250Q83 261 91 266Q664 540 678 540Q681 540 687 534T694 519T687 505Q686 504 417 376L151 250L417 124Q686 -4 687 -5Q694 -11 694 -19Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-30” d=“M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-4E" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-31" x=“1136” y="-213"></use>
<use xlink:href="#E1-MJMAIN-3C" x=“1535” y=“0”></use>
<use xlink:href="#E1-MJMAIN-30" x=“2591” y=“0”></use>
</g>
</svg> ou <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“4.778ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 2057.3 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> > 60</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMAIN-3E” d=“M84 520Q84 528 88 533T96 539L99 540Q106 540 253 471T544 334L687 265Q694 260 694 250T687 235Q685 233 395 96L107 -40H101Q83 -38 83 -20Q83 -19 83 -17Q82 -10 98 -1Q117 9 248 71Q326 108 378 132L626 250L378 368Q90 504 86 509Q84 513 84 520Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-36” d=“M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-30” d=“M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMAIN-3E" x=“0” y=“0”></use>
<g transform=“translate(1056,0)”>
<use xlink:href="#E1-MJMAIN-36"></use>
<use xlink:href="#E1-MJMAIN-30" x=“500” y=“0”></use>
</g>
</g>
</svg>).</p>
<p>Show?</p>

Passo 3

<p><b>(c) para </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“7.81ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 3362.6 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> N = 30</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHBI-4E” d=“M258 624H235Q214 624 209 626T199 639Q203 678 216 684Q220 686 344 686H434Q464 686 477 680Q480 677 607 454Q738 227 739 227Q742 227 789 418T836 618Q836 620 835 620L821 622Q811 622 779 624Q755 624 749 625T740 632Q737 635 737 644Q737 656 742 669T754 685Q755 685 757 685T763 686Q768 686 803 685T890 684Q925 684 951 684T990 685T1006 686Q1014 686 1016 684Q1027 679 1027 668Q1023 632 1011 626Q1007 624 978 624Q912 622 907 617Q907 616 831 314T753 8Q749 0 723 0H712Q699 0 692 7Q692 8 671 44T607 155T526 296L361 580L296 323Q234 74 234 68T302 62H307Q334 62 334 44Q330 6 317 2L313 0L280 1Q260 2 181 2Q125 2 96 1T63 0Q48 0 43 15Q43 19 47 35Q52 55 57 58T94 62Q147 64 164 69L233 345Q302 619 302 622Q302 624 258 624Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-33” d=“M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-30” d=“M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHBI-4E" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1305” y=“0”></use>
<g transform=“translate(2361,0)”>
<use xlink:href="#E1-MJMAIN-33"></use>
<use xlink:href="#E1-MJMAIN-30" x=“500” y=“0”></use>
</g>
</g>
</svg><b>:</b></p>
<ul>
<li><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“18.576ex” height=“2.843ex” style=“vertical-align: -0.838ex;” viewBox=“0 -863.1 7998.1 1223.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> μ = 30 × 2 / 3 = 20</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-3BC” d=“M58 -216Q44 -216 34 -208T23 -186Q23 -176 96 116T173 414Q186 442 219 442Q231 441 239 435T249 423T251 413Q251 401 220 279T187 142Q185 131 185 107V99Q185 26 252 26Q261 26 270 27T287 31T302 38T315 45T327 55T338 65T348 77T356 88T365 100L372 110L408 253Q444 395 448 404Q461 431 491 431Q504 431 512 424T523 412T525 402L449 84Q448 79 448 68Q448 43 455 35T476 26Q485 27 496 35Q517 55 537 131Q543 151 547 152Q549 153 557 153H561Q580 153 580 144Q580 138 575 117T555 63T523 13Q510 0 491 -8Q483 -10 467 -10Q446 -10 429 -4T402 11T385 29T376 44T374 51L368 45Q362 39 350 30T324 12T288 -4T246 -11Q199 -11 153 12L129 -85Q108 -167 104 -180T92 -202Q76 -216 58 -216Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-33” d=“M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-30” d=“M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-D7” d=“M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-32” d=“M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2F” d=“M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-3BC" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-3D" x=“881” y=“0”></use>
<g transform=“translate(1937,0)”>
<use xlink:href="#E1-MJMAIN-33"></use>
<use xlink:href="#E1-MJMAIN-30" x=“500” y=“0”></use>
</g>
<use xlink:href="#E1-MJMAIN-D7" x=“3160” y=“0”></use>
<use xlink:href="#E1-MJMAIN-32" x=“4161” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2F" x=“4662” y=“0”></use>
<use xlink:href="#E1-MJMAIN-33" x=“5162” y=“0”></use>
<use xlink:href="#E1-MJMAIN-3D" x=“5940” y=“0”></use>
<g transform=“translate(6997,0)”>
<use xlink:href="#E1-MJMAIN-32"></use>
<use xlink:href="#E1-MJMAIN-30" x=“500” y=“0”></use>
</g>
</g>
</svg></li>
<li><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“30.279ex” height=“3.009ex” style=“vertical-align: -0.838ex;” viewBox=“0 -934.9 13036.9 1295.7” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> σ 2 = 30 × 2 / 9 = 60 / 9 ≈ 6.667</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-3C3” d=“M184 -11Q116 -11 74 34T31 147Q31 247 104 333T274 430Q275 431 414 431H552Q553 430 555 429T559 427T562 425T565 422T567 420T569 416T570 412T571 407T572 401Q572 357 507 357Q500 357 490 357T476 358H416L421 348Q439 310 439 263Q439 153 359 71T184 -11ZM361 278Q361 358 276 358Q152 358 115 184Q114 180 114 178Q106 141 106 117Q106 67 131 47T188 26Q242 26 287 73Q316 103 334 153T356 233T361 278Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-32” d=“M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-33” d=“M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-30” d=“M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-D7” d=“M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2F” d=“M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-39” d=“M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-36” d=“M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2248” d=“M55 319Q55 360 72 393T114 444T163 472T205 482Q207 482 213 482T223 483Q262 483 296 468T393 413L443 381Q502 346 553 346Q609 346 649 375T694 454Q694 465 698 474T708 483Q722 483 722 452Q722 386 675 338T555 289Q514 289 468 310T388 357T308 404T224 426Q164 426 125 393T83 318Q81 289 69 289Q55 289 55 319ZM55 85Q55 126 72 159T114 210T163 238T205 248Q207 248 213 248T223 249Q262 249 296 234T393 179L443 147Q502 112 553 112Q609 112 649 141T694 220Q694 249 708 249T722 217Q722 153 675 104T555 55Q514 55 468 76T388 123T308 170T224 192Q164 192 125 159T83 84Q80 55 69 55Q55 55 55 85Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2E” d=“M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-37” d=“M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-3C3" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-32" x=“810” y=“513”></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1304” y=“0”></use>
<g transform=“translate(2360,0)”>
<use xlink:href="#E1-MJMAIN-33"></use>
<use xlink:href="#E1-MJMAIN-30" x=“500” y=“0”></use>
</g>
<use xlink:href="#E1-MJMAIN-D7" x=“3584” y=“0”></use>
<use xlink:href="#E1-MJMAIN-32" x=“4584” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2F" x=“5085” y=“0”></use>
<use xlink:href="#E1-MJMAIN-39" x=“5585” y=“0”></use>
<use xlink:href="#E1-MJMAIN-3D" x=“6364” y=“0”></use>
<g transform=“translate(7420,0)”>
<use xlink:href="#E1-MJMAIN-36"></use>
<use xlink:href="#E1-MJMAIN-30" x=“500” y=“0”></use>
</g>
<use xlink:href="#E1-MJMAIN-2F" x=“8421” y=“0”></use>
<use xlink:href="#E1-MJMAIN-39" x=“8921” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2248" x=“9700” y=“0”></use>
<g transform=“translate(10756,0)”>
<use xlink:href="#E1-MJMAIN-36"></use>
<use xlink:href="#E1-MJMAIN-2E" x=“500” y=“0”></use>
<use xlink:href="#E1-MJMAIN-36" x=“779” y=“0”></use>
<use xlink:href="#E1-MJMAIN-36" x=“1279” y=“0”></use>
<use xlink:href="#E1-MJMAIN-37" x=“1780” y=“0”></use>
</g>
</g>
</svg></li>
<li>
<svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“9.725ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 4187.1 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> σ ≈ 2.582</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-3C3” d=“M184 -11Q116 -11 74 34T31 147Q31 247 104 333T274 430Q275 431 414 431H552Q553 430 555 429T559 427T562 425T565 422T567 420T569 416T570 412T571 407T572 401Q572 357 507 357Q500 357 490 357T476 358H416L421 348Q439 310 439 263Q439 153 359 71T184 -11ZM361 278Q361 358 276 358Q152 358 115 184Q114 180 114 178Q106 141 106 117Q106 67 131 47T188 26Q242 26 287 73Q316 103 334 153T356 233T361 278Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2248” d=“M55 319Q55 360 72 393T114 444T163 472T205 482Q207 482 213 482T223 483Q262 483 296 468T393 413L443 381Q502 346 553 346Q609 346 649 375T694 454Q694 465 698 474T708 483Q722 483 722 452Q722 386 675 338T555 289Q514 289 468 310T388 357T308 404T224 426Q164 426 125 393T83 318Q81 289 69 289Q55 289 55 319ZM55 85Q55 126 72 159T114 210T163 238T205 248Q207 248 213 248T223 249Q262 249 296 234T393 179L443 147Q502 112 553 112Q609 112 649 141T694 220Q694 249 708 249T722 217Q722 153 675 104T555 55Q514 55 468 76T388 123T308 170T224 192Q164 192 125 159T83 84Q80 55 69 55Q55 55 55 85Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-32” d=“M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2E” d=“M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-35” d=“M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-38” d=“M70 417T70 494T124 618T248 666Q319 666 374 624T429 515Q429 485 418 459T392 417T361 389T335 371T324 363L338 354Q352 344 366 334T382 323Q457 264 457 174Q457 95 399 37T249 -22Q159 -22 101 29T43 155Q43 263 172 335L154 348Q133 361 127 368Q70 417 70 494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-3C3" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2248" x=“850” y=“0”></use>
<g transform=“translate(1906,0)”>
<use xlink:href="#E1-MJMAIN-32"></use>
<use xlink:href="#E1-MJMAIN-2E" x=“500” y=“0”></use>
<use xlink:href="#E1-MJMAIN-35" x=“779” y=“0”></use>
<use xlink:href="#E1-MJMAIN-38" x=“1279” y=“0”></use>
<use xlink:href="#E1-MJMAIN-32" x=“1780” y=“0”></use>
</g>
</g>
</svg>.</li>
<li>Ainda temos <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“8.656ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 3727.1 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> N p = 20</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-70” d=“M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-32” d=“M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-30” d=“M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-4E" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMATHI-70" x=“888” y=“0”></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1669” y=“0”></use>
<g transform=“translate(2726,0)”>
<use xlink:href="#E1-MJMAIN-32"></use>
<use xlink:href="#E1-MJMAIN-30" x=“500” y=“0”></use>
</g>
</g>
</svg>, <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“8.557ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 3684.1 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> N q = 10</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-71” d=“M33 157Q33 258 109 349T280 441Q340 441 372 389Q373 390 377 395T388 406T404 418Q438 442 450 442Q454 442 457 439T460 434Q460 425 391 149Q320 -135 320 -139Q320 -147 365 -148H390Q396 -156 396 -157T393 -175Q389 -188 383 -194H370Q339 -192 262 -192Q234 -192 211 -192T174 -192T157 -193Q143 -193 143 -185Q143 -182 145 -170Q149 -154 152 -151T172 -148Q220 -148 230 -141Q238 -136 258 -53T279 32Q279 33 272 29Q224 -10 172 -10Q117 -10 75 30T33 157ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-30” d=“M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-4E" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMATHI-71" x=“888” y=“0”></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1626” y=“0”></use>
<g transform=“translate(2683,0)”>
<use xlink:href="#E1-MJMAIN-31"></use>
<use xlink:href="#E1-MJMAIN-30" x=“500” y=“0”></use>
</g>
</g>
</svg>, ambos <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“3.616ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 1556.8 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> > 5</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMAIN-3E” d=“M84 520Q84 528 88 533T96 539L99 540Q106 540 253 471T544 334L687 265Q694 260 694 250T687 235Q685 233 395 96L107 -40H101Q83 -38 83 -20Q83 -19 83 -17Q82 -10 98 -1Q117 9 248 71Q326 108 378 132L626 250L378 368Q90 504 86 509Q84 513 84 520Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-35” d=“M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMAIN-3E" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-35" x=“1056” y=“0”></use>
</g>
</svg>, então aproximação razoável, mas a assimetria da binomial <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“9.049ex” height=“2.843ex” style=“vertical-align: -0.838ex;” viewBox=“0 -863.1 3896.1 1223.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> p ≠ 0.5 </title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMAIN-28” d=“M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z”></path>
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<g transform=“translate(389,0)”>
<use xlink:href="#E1-MJMATHI-70" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2260" x=“781” y=“0”></use>
<g transform=“translate(1837,0)”>
<use xlink:href="#E1-MJMAIN-30"></use>
<use xlink:href="#E1-MJMAIN-2E" x=“500” y=“0”></use>
<use xlink:href="#E1-MJMAIN-35" x=“779” y=“0”></use>
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<use xlink:href="#E1-MJMAIN-29" x=“3506” y=“0”></use>
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</svg> já é mais perceptível. A gaussiana é simétrica em torno da média, a binomial não exatamente. Visualmente, o ajuste ainda é bom perto do pico, mas nas caudas há pequenos desvios.</li>
</ul>
<p><b>(c) para </b><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“7.81ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 3362.6 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> N = 15</title>
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<path stroke-width=“1” id=“E1-MJMATHBI-4E” d=“M258 624H235Q214 624 209 626T199 639Q203 678 216 684Q220 686 344 686H434Q464 686 477 680Q480 677 607 454Q738 227 739 227Q742 227 789 418T836 618Q836 620 835 620L821 622Q811 622 779 624Q755 624 749 625T740 632Q737 635 737 644Q737 656 742 669T754 685Q755 685 757 685T763 686Q768 686 803 685T890 684Q925 684 951 684T990 685T1006 686Q1014 686 1016 684Q1027 679 1027 668Q1023 632 1011 626Q1007 624 978 624Q912 622 907 617Q907 616 831 314T753 8Q749 0 723 0H712Q699 0 692 7Q692 8 671 44T607 155T526 296L361 580L296 323Q234 74 234 68T302 62H307Q334 62 334 44Q330 6 317 2L313 0L280 1Q260 2 181 2Q125 2 96 1T63 0Q48 0 43 15Q43 19 47 35Q52 55 57 58T94 62Q147 64 164 69L233 345Q302 619 302 622Q302 624 258 624Z”></path>
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<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”></path>
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<use xlink:href="#E1-MJMAIN-35" x=“500” y=“0”></use>
</g>
</g>
</svg><b>:</b></p>
<ul>
<li><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“18.576ex” height=“2.843ex” style=“vertical-align: -0.838ex;” viewBox=“0 -863.1 7998.1 1223.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> μ = 15 × 2 / 3 = 10</title>
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<path stroke-width=“1” id=“E1-MJMAIN-32” d=“M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z”></path>
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<use xlink:href="#E1-MJMAIN-30" x=“500” y=“0”></use>
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</g>
</svg></li>
<li><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“30.279ex” height=“3.009ex” style=“vertical-align: -0.838ex;” viewBox=“0 -934.9 13036.9 1295.7” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> σ 2 = 15 × 2 / 9 = 30 / 9 ≈ 3.333</title>
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<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-32" x=“810” y=“513”></use>
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<use xlink:href="#E1-MJMAIN-30" x=“500” y=“0”></use>
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<use xlink:href="#E1-MJMAIN-2F" x=“8421” y=“0”></use>
<use xlink:href="#E1-MJMAIN-39" x=“8921” y=“0”></use>
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<use xlink:href="#E1-MJMAIN-33" x=“779” y=“0”></use>
<use xlink:href="#E1-MJMAIN-33" x=“1279” y=“0”></use>
<use xlink:href="#E1-MJMAIN-33" x=“1780” y=“0”></use>
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</svg></li>
<li>
<svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“9.725ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 4187.1 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> σ ≈ 1.826</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-3C3” d=“M184 -11Q116 -11 74 34T31 147Q31 247 104 333T274 430Q275 431 414 431H552Q553 430 555 429T559 427T562 425T565 422T567 420T569 416T570 412T571 407T572 401Q572 357 507 357Q500 357 490 357T476 358H416L421 348Q439 310 439 263Q439 153 359 71T184 -11ZM361 278Q361 358 276 358Q152 358 115 184Q114 180 114 178Q106 141 106 117Q106 67 131 47T188 26Q242 26 287 73Q316 103 334 153T356 233T361 278Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2248” d=“M55 319Q55 360 72 393T114 444T163 472T205 482Q207 482 213 482T223 483Q262 483 296 468T393 413L443 381Q502 346 553 346Q609 346 649 375T694 454Q694 465 698 474T708 483Q722 483 722 452Q722 386 675 338T555 289Q514 289 468 310T388 357T308 404T224 426Q164 426 125 393T83 318Q81 289 69 289Q55 289 55 319ZM55 85Q55 126 72 159T114 210T163 238T205 248Q207 248 213 248T223 249Q262 249 296 234T393 179L443 147Q502 112 553 112Q609 112 649 141T694 220Q694 249 708 249T722 217Q722 153 675 104T555 55Q514 55 468 76T388 123T308 170T224 192Q164 192 125 159T83 84Q80 55 69 55Q55 55 55 85Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2E” d=“M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-38” d=“M70 417T70 494T124 618T248 666Q319 666 374 624T429 515Q429 485 418 459T392 417T361 389T335 371T324 363L338 354Q352 344 366 334T382 323Q457 264 457 174Q457 95 399 37T249 -22Q159 -22 101 29T43 155Q43 263 172 335L154 348Q133 361 127 368Q70 417 70 494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-32” d=“M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-36” d=“M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-3C3" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2248" x=“850” y=“0”></use>
<g transform=“translate(1906,0)”>
<use xlink:href="#E1-MJMAIN-31"></use>
<use xlink:href="#E1-MJMAIN-2E" x=“500” y=“0”></use>
<use xlink:href="#E1-MJMAIN-38" x=“779” y=“0”></use>
<use xlink:href="#E1-MJMAIN-32" x=“1279” y=“0”></use>
<use xlink:href="#E1-MJMAIN-36" x=“1780” y=“0”></use>
</g>
</g>
</svg>.</li>
<li>Aqui <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“7.394ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 3183.6 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> N q = 5</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-71” d=“M33 157Q33 258 109 349T280 441Q340 441 372 389Q373 390 377 395T388 406T404 418Q438 442 450 442Q454 442 457 439T460 434Q460 425 391 149Q320 -135 320 -139Q320 -147 365 -148H390Q396 -156 396 -157T393 -175Q389 -188 383 -194H370Q339 -192 262 -192Q234 -192 211 -192T174 -192T157 -193Q143 -193 143 -185Q143 -182 145 -170Q149 -154 152 -151T172 -148Q220 -148 230 -141Q238 -136 258 -53T279 32Q279 33 272 29Q224 -10 172 -10Q117 -10 75 30T33 157ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-35” d=“M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-4E" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMATHI-71" x=“888” y=“0”></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1626” y=“0”></use>
<use xlink:href="#E1-MJMAIN-35" x=“2683” y=“0”></use>
</g>
</svg> (limite da regra prática <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“7.394ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 3183.6 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> N q ≥ 5</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-71” d=“M33 157Q33 258 109 349T280 441Q340 441 372 389Q373 390 377 395T388 406T404 418Q438 442 450 442Q454 442 457 439T460 434Q460 425 391 149Q320 -135 320 -139Q320 -147 365 -148H390Q396 -156 396 -157T393 -175Q389 -188 383 -194H370Q339 -192 262 -192Q234 -192 211 -192T174 -192T157 -193Q143 -193 143 -185Q143 -182 145 -170Q149 -154 152 -151T172 -148Q220 -148 230 -141Q238 -136 258 -53T279 32Q279 33 272 29Q224 -10 172 -10Q117 -10 75 30T33 157ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2265” d=“M83 616Q83 624 89 630T99 636Q107 636 253 568T543 431T687 361Q694 356 694 346T687 331Q685 329 395 192L107 56H101Q83 58 83 76Q83 77 83 79Q82 86 98 95Q117 105 248 167Q326 204 378 228L626 346L360 472Q291 505 200 548Q112 589 98 597T83 616ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-35” d=“M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-4E" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMATHI-71" x=“888” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2265" x=“1626” y=“0”></use>
<use xlink:href="#E1-MJMAIN-35" x=“2683” y=“0”></use>
</g>
</svg>), então a aproximação começa a ficar grosseira. A binomial é visivelmente assimétrica, a gaussiana simétrica não captura bem a cauda esquerda (menor <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.92ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 1257.4 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> N 1 </title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-4E" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-31" x=“1136” y="-213"></use>
</g>
</svg>) e a cauda direita (maior <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“2.92ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 1257.4 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> N 1 </title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-4E" x=“0” y=“0”></use>
<use transform=“scale(0.707)” xlink:href="#E1-MJMAIN-31" x=“1136” y="-213"></use>
</g>
</svg>).</li>
</ul>
<p><b>Conclusões qualitativas dos gráficos:</b></p>
<ul>
<li>Para <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“7.487ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 3223.6 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> N = 60</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-36” d=“M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-30” d=“M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-4E" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1166” y=“0”></use>
<g transform=“translate(2222,0)”>
<use xlink:href="#E1-MJMAIN-36"></use>
<use xlink:href="#E1-MJMAIN-30" x=“500” y=“0”></use>
</g>
</g>
</svg>: excelente concordância entre binomial e gaussiana.</li>
<li>Para <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“7.487ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 3223.6 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> N = 30</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-33” d=“M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-30” d=“M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-4E" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-3D" x=“1166” y=“0”></use>
<g transform=“translate(2222,0)”>
<use xlink:href="#E1-MJMAIN-33"></use>
<use xlink:href="#E1-MJMAIN-30" x=“500” y=“0”></use>
</g>
</g>
</svg>: boa concordância, pequenos desvios nas caudas.</li>
<li>Para <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“7.487ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 3223.6 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> N = 15</title>
<defs aria-hidden=“true”>
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</g>
</svg>: concordância apenas grosseira, especialmente nas caudas; a assimetria da binomial é perceptível.</li>
</ul>
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”></p>
<p>E fim! Entendeu tudo? Responde Aí!</p>

Resposta

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”></p>

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