1. Satistics: Normal distributionYou work in the Volkswagen emissions testing department and test 100 diesel engine cars to determine that the average NOx emissions are 0.270 g/km with a standard deviation of 0.045 g/km. If Volkswagen sold 650,000 diesel cars and the law says you cannot emit more than 0.180 g/km, how many cars broke the law? (For full credit, you must show your calculations and have the right number of significant digits and the right units.) Areas under the StandardNormal Curve from 0 to z00.01.02.03.04.05.06.07.08.09.023 90636027 9067 5.106 4144 3031 9.012 0 .016O.055 70.0.0000004 0.008.0.019 9035 90.1039 80433.047 8.051 7059 6071 4.075 40.2.079 3.083 2.087 1.091 0.094 8098 7102 6.110 3.114 10.3.117 9 .121 7125 5 .129 3.133 1136 8140 6.148 0.151 70.4.155 4.159 1.162 8 .166 4.170 0173 6177 2180 8.184 1187 9.198 5 .201 9.232 4212 3245 4215 7248 60.5.191 5.195 0.205 4208 8219 0222 40.6.225 8.229 1.235 7.238 92422251 8254 90.7.258 0.261 2.264 2.267 3.270 4273 4276 4279 4282 3285 2307 8334 0310 6336 50.8.288 1.291 0.293 9.296 7.299 6302 3305 1.313 30.9.315 9.318 6.321 2.323 8.326 4.328 9331 5.338 9.343 8 .346 1.3a 6.388 81.0.341 3.348 5.350 8353 1355 4357 7359 9.362 11.1.364 3.366 5.370 8.372 9374 9379 0398 0377 0381 0383 01.2.384 9.386 9.390 7.392 5.394 4396 2399 7401 51.3.403 2.4049.406 6.409 94131427 9.408 2411 5414 7416 2430 6417 71.4.419 2420 7.422 2.423 6.425 1426 5429 2431 91.5.433 2 .4345.435 7440 6451 5.437 0.438 2439 4441 8452 5442 9444 11.6445 2 4463447 4.450 5459 9448 4.449 5453 5454 51.7.4555456 4457 3458 2459 1460 8461 6462 5 .4633469 9 470 6.476 11.8.464 1464 9465 6466 4.467 1467 8468 6469 31.9.471 3471 9472 6473 2473 8474 4475 0475 6.476 72.0477 2477 8478 3478 8.479 3479 8480 3480 8481 2481 7

X follows a Normal distribution with mean = 0.27 and S.D = 0.045 Then z=(x-mean)/SD =…

Answered: You work in the Volkswagen emissions…

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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1. Satistics: Normal distribution

You work in the Volkswagen emissions testing department and test 100 diesel engine cars to determine that the average NOx emissions are 0.270 g/km with a standard deviation of 0.045 g/km. If Volkswagen sold 650,000 diesel cars and the law says you cannot emit more than 0.180 g/km, how many cars broke the law? (For full credit, you must show your calculations and have the right number of significant digits and the right units.)

Areas under the Standard
Normal Curve from 0 to z
00
.01
.02
.03
.04
.05
.06
.07
.08
.09
.023 9
0636
027 9
067 5
.106 4
144 3
031 9
.012 0 .016O
.055 7
0.0
.0000
004 0
.008.0
.019 9
035 9
0.1
039 8
0433
.047 8
.051 7
059 6
071 4
.075 4
0.2
.079 3
.083 2
.087 1
.091 0
.094 8
098 7
102 6
.110 3
.114 1
0.3
.117 9 .121 7
125 5 .129 3
.133 1
136 8
140 6
.148 0
.151 7
0.4
.155 4
.159 1
.162 8 .166 4
.170 0
173 6
177 2
180 8
.184 1
187 9
.198 5 .201 9
.232 4
212 3
245 4
215 7
248 6
0.5
.191 5
.195 0
.205 4
208 8
219 0
222 4
0.6
.225 8
.229 1
.235 7
.238 9
2422
251 8
254 9
0.7
.258 0
.261 2
.264 2
.267 3
.270 4
273 4
276 4
279 4
282 3
285 2
307 8
334 0
310 6
336 5
0.8
.288 1
.291 0
.293 9
.296 7
.299 6
302 3
305 1
.313 3
0.9
.315 9
.318 6
.321 2
.323 8
.326 4
.328 9
331 5
.338 9
.343 8 .346 1
.3a 6
.388 8
1.0
.341 3
.348 5
.350 8
353 1
355 4
357 7
359 9
.362 1
1.1
.364 3
.366 5
.370 8
.372 9
374 9
379 0
398 0
377 0
381 0
383 0
1.2
.384 9
.386 9
.390 7
.392 5
.394 4
396 2
399 7
401 5
1.3
.403 2.4049
.406 6
.409 9
4131
427 9
.408 2
411 5
414 7
416 2
430 6
417 7
1.4
.419 2
420 7
.422 2
.423 6
.425 1
426 5
429 2
431 9
1.5
.433 2 .4345
.435 7
440 6
451 5
.437 0
.438 2
439 4
441 8
452 5
442 9
444 1
1.6
445 2 4463
447 4
.450 5
459 9
448 4
.449 5
453 5
454 5
1.7
.4555
456 4
457 3
458 2
459 1
460 8
461 6
462 5 .4633
469 9 470 6
.476 1
1.8
.464 1
464 9
465 6
466 4
.467 1
467 8
468 6
469 3
1.9
.471 3
471 9
472 6
473 2
473 8
474 4
475 0
475 6
.476 7
2.0
477 2
477 8
478 3
478 8
.479 3
479 8
480 3
480 8
481 2
481 7

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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