Areas under the Normal Curve The column under A gives the proportion of the area under the entire curve that is betweenz=0 and a positive value of z. Because the curve is symmetric about 0, the area between z=0 and a negative value of z can I found by using the corresponding positive value of z. 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.000 0.004 0.008 0.012 0.016 0.020 0.024 0.028 0.032 0.036 0.040 0.044 0.048 0.052 0.056 0.060 0.064 0.067 0.071 0.075 0.079 0.083 0.087 0.091 0.095 0.099 0.103 0.106 0.110 0.114 0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.40 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.50 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.118 0.122 0.126 0.129 0.133 0.137 0.141 0.144 0.148 0.152 0.155 0.159 0.163 0.166 0.170 0.174 0.177 0.181 0.184 0.188 0.191 0.195 0.198 0.202 0.205 0.209 0.212 0.216 0.219 0.222 0.60 0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69 0.70 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 0.80 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.226 0.229 0.232 0.236 0.239 0.242 0.245 0.249 0.252 0.255 0.258 0.261 0.264 0.267 0.270 0.273 0.276 0.279 0.282 0.285 0.288 0.291 0.294 0.297 0.300 0.302 0.305 0.308 0.311 0.313 0.90 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 1.11 1.12 1.13 1.14 1.15 1.16 1.17 1.18 1.19 0.316 0.319 0.321 0.324 0.326 0.329 0.331 0.334 0.336 0.339 0.341 0.344 0.346 0.348 0.351 0.353 0.355 0.358 0.360 0.362 0.364 0.367 0.369 0.371 0.373 0.375 0.377 0.379 0.381 0.383 1.20 1.21 1.22 1.23 1.24 1.25 1.26 1.27 1.28 1.29 1.30 1.31 1.32 1.33 1.34 1.35 1.36 1.37 1.38 1.39 1.40 1.41 1.42 1.43 1.44 1.45 1.46 1.47 1.48 1.49 0.385 0.387 0.389 0.391 0.393 0.394 0.396 0.398 0.400 0.401 0.403 0.405 0.407 0.408 0.410 0.411 0.413 0.415 0.416 0.418 0.419 0.421 0.422 0.424 0.425 0.426 0.428 0.429 0.431 0.432 1.50 1.51 1.52 1.53 1.54 1.55 1.56 1.57 1.58 1.59 1.60 1.61 1.62 1.63 1.64 1.65 1.66 1.67 1.68 1.69 1.70 1.71 1.72 1.73 1.74 1.75 1.76 1.77 1.78 1.79 0.433 0.434 0.436 0.437 0.438 0.439 0.441 0.442 0.443 0.444 0.445 0.446 0.447 0.448 0.449 0.451 0.452 0.453 0.454 0.454 0.455 0.456 0.457 0.458 0.459 0.460 0.461 0.462 0.462 0.463 Areas under the Normal Curve The column under A gives the proportion of the area under the entire curve that is between z=0 and a positive value of z. Because the curve is symmetric about 0, the area betweenz=0 and a negative value of z can be found by using the corresponding positive value of z. こ 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 3.30 3.31 3.32 3.33 3.34 3.35 3.36 3.37 3.38 3.39 3.40 3.41 3.42 3.43 3.44 3.45 3.46 3.47 3.48 3.49 3.50 3.51 3.52 3.53 3.54 3.55 3.56 3.57 3.58 3.59 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.482 2.40 0.483 2.41 0.483 2.42 0.483 2.43 0.484 2.44 0.484 2.45 0.485 2.46 2.47 0.485 0.485 2.48 2.49 0.486 0.486 2.50 0.492 0.492 0.492 0.492 0.493 0.493 0.493 0.493 0.493 0.494 0.494 0.494 0.494 0.494 0.494 0.495 0.495 0.495 0.495 0.495 0.495 0.495 0.496 0.496 0.496 0.496 0.496 0.496 0.496 0.496 2.70 2.71 2.72 2.73 2.74 2.75 2.76 2.77 2.78 2.79 2.80 2.81 2.82 2.83 2.84 2.85 2.86 2.87 2.88 2.89 2.90 2.91 2.92 2.93 2.94 2.95 2.96 2.97 2.98 2.99 0.497 3.00 1.80 1.81 1.82 1.83 1.84 1.85 1.86 1.87 1.88 1.89 1.90 1.91 1.92 1.93 1.94 1.95 1.96 1.97 1.98 1.99 2.00 2.01 2.02 2.03 2.04 2.05 2.06 2.07 2.08 2.09 0.464 0.465 0.466 0.466 0.467 0.468 0.469 0.469 0.470 0.471 0.471 0.472 0.473 0.473 0.474 0.474 0.475 0.476 0.476 0.477 0.477 0.478 0.478 0.479 0.479 0.480 0.480 0.481 0.481 0.482 2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18 2.19 2.20 2.21 2.22 2.23 2.24 2.25 2.26 2.27 2.28 2.29 2.30 2.31 2.32 2.33 2.34 2.35 2.36 2.37 2.38 2.39 0.497 3.01 0.497 3.02 0.497 3.03 0.497 3.04 0.497 3.05 0.497 3.06 0.497 3.07 0.497 3.08 0.497 3.09 0.497 3.10 3.11 0.498 3.12 0.498 0.498 3.13 0.498 3.14 3.15 0.498 0.498 3.16 0.498 3.17 3.18 0.498 0.498 3.19 0.498 3.20 0.498 3.21 0.498 3.22 0.498 3.23 0.498 3.24 0.498 3.25 0.498 3.26 0.499 3.27 0.499 3.28 0.499 3.29 0.486 2.51 0.487 2.52 0.487 2.53 0.487 0.488 2.54 2.55 0.488 2.56 0.488 0.489 0.489 0.489 2.57 2.58 2.59 2.60 0.490 2.61 0.490 0.490 0.490 0.491 0.491 2.62 2.63 2.64 2.65 2.66 0.491 2.67 0.491 0.492 2.68 2.69

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Related questions
Topic Video
Question

Suppose 140 geology students measure the mass of an ore sample. Due to human error and limitaions in the reliability of the balance, not all the readins are equal. The results are found to closley approxiamate a normal curve, with mean 88 g and standard deviation 1 g. Use the symmetry of the normal curve and the emirical rule as needed to estimate the number of students reporting readings more than 88 g.

Areas under the Normal Curve
The column under A gives the
proportion of the area under the
entire curve that is betweenz=0
and a positive value of z.
Because the curve is symmetric
about 0, the area between z=0
and a negative value of z can I
found by using the corresponding
positive value of z.
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
0.11
0.12
0.13
0.14
0.15
0.16
0.17
0.18
0.19
0.20
0.21
0.22
0.23
0.24
0.25
0.26
0.27
0.28
0.29
0.000
0.004
0.008
0.012
0.016
0.020
0.024
0.028
0.032
0.036
0.040
0.044
0.048
0.052
0.056
0.060
0.064
0.067
0.071
0.075
0.079
0.083
0.087
0.091
0.095
0.099
0.103
0.106
0.110
0.114
0.30
0.31
0.32
0.33
0.34
0.35
0.36
0.37
0.38
0.39
0.40
0.41
0.42
0.43
0.44
0.45
0.46
0.47
0.48
0.49
0.50
0.51
0.52
0.53
0.54
0.55
0.56
0.57
0.58
0.59
0.118
0.122
0.126
0.129
0.133
0.137
0.141
0.144
0.148
0.152
0.155
0.159
0.163
0.166
0.170
0.174
0.177
0.181
0.184
0.188
0.191
0.195
0.198
0.202
0.205
0.209
0.212
0.216
0.219
0.222
0.60
0.61
0.62
0.63
0.64
0.65
0.66
0.67
0.68
0.69
0.70
0.71
0.72
0.73
0.74
0.75
0.76
0.77
0.78
0.79
0.80
0.81
0.82
0.83
0.84
0.85
0.86
0.87
0.88
0.89
0.226
0.229
0.232
0.236
0.239
0.242
0.245
0.249
0.252
0.255
0.258
0.261
0.264
0.267
0.270
0.273
0.276
0.279
0.282
0.285
0.288
0.291
0.294
0.297
0.300
0.302
0.305
0.308
0.311
0.313
0.90
0.91
0.92
0.93
0.94
0.95
0.96
0.97
0.98
0.99
1.00
1.01
1.02
1.03
1.04
1.05
1.06
1.07
1.08
1.09
1.10
1.11
1.12
1.13
1.14
1.15
1.16
1.17
1.18
1.19
0.316
0.319
0.321
0.324
0.326
0.329
0.331
0.334
0.336
0.339
0.341
0.344
0.346
0.348
0.351
0.353
0.355
0.358
0.360
0.362
0.364
0.367
0.369
0.371
0.373
0.375
0.377
0.379
0.381
0.383
1.20
1.21
1.22
1.23
1.24
1.25
1.26
1.27
1.28
1.29
1.30
1.31
1.32
1.33
1.34
1.35
1.36
1.37
1.38
1.39
1.40
1.41
1.42
1.43
1.44
1.45
1.46
1.47
1.48
1.49
0.385
0.387
0.389
0.391
0.393
0.394
0.396
0.398
0.400
0.401
0.403
0.405
0.407
0.408
0.410
0.411
0.413
0.415
0.416
0.418
0.419
0.421
0.422
0.424
0.425
0.426
0.428
0.429
0.431
0.432
1.50
1.51
1.52
1.53
1.54
1.55
1.56
1.57
1.58
1.59
1.60
1.61
1.62
1.63
1.64
1.65
1.66
1.67
1.68
1.69
1.70
1.71
1.72
1.73
1.74
1.75
1.76
1.77
1.78
1.79
0.433
0.434
0.436
0.437
0.438
0.439
0.441
0.442
0.443
0.444
0.445
0.446
0.447
0.448
0.449
0.451
0.452
0.453
0.454
0.454
0.455
0.456
0.457
0.458
0.459
0.460
0.461
0.462
0.462
0.463
Transcribed Image Text:Areas under the Normal Curve The column under A gives the proportion of the area under the entire curve that is betweenz=0 and a positive value of z. Because the curve is symmetric about 0, the area between z=0 and a negative value of z can I found by using the corresponding positive value of z. 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.000 0.004 0.008 0.012 0.016 0.020 0.024 0.028 0.032 0.036 0.040 0.044 0.048 0.052 0.056 0.060 0.064 0.067 0.071 0.075 0.079 0.083 0.087 0.091 0.095 0.099 0.103 0.106 0.110 0.114 0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.40 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.50 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.118 0.122 0.126 0.129 0.133 0.137 0.141 0.144 0.148 0.152 0.155 0.159 0.163 0.166 0.170 0.174 0.177 0.181 0.184 0.188 0.191 0.195 0.198 0.202 0.205 0.209 0.212 0.216 0.219 0.222 0.60 0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69 0.70 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 0.80 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.226 0.229 0.232 0.236 0.239 0.242 0.245 0.249 0.252 0.255 0.258 0.261 0.264 0.267 0.270 0.273 0.276 0.279 0.282 0.285 0.288 0.291 0.294 0.297 0.300 0.302 0.305 0.308 0.311 0.313 0.90 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 1.11 1.12 1.13 1.14 1.15 1.16 1.17 1.18 1.19 0.316 0.319 0.321 0.324 0.326 0.329 0.331 0.334 0.336 0.339 0.341 0.344 0.346 0.348 0.351 0.353 0.355 0.358 0.360 0.362 0.364 0.367 0.369 0.371 0.373 0.375 0.377 0.379 0.381 0.383 1.20 1.21 1.22 1.23 1.24 1.25 1.26 1.27 1.28 1.29 1.30 1.31 1.32 1.33 1.34 1.35 1.36 1.37 1.38 1.39 1.40 1.41 1.42 1.43 1.44 1.45 1.46 1.47 1.48 1.49 0.385 0.387 0.389 0.391 0.393 0.394 0.396 0.398 0.400 0.401 0.403 0.405 0.407 0.408 0.410 0.411 0.413 0.415 0.416 0.418 0.419 0.421 0.422 0.424 0.425 0.426 0.428 0.429 0.431 0.432 1.50 1.51 1.52 1.53 1.54 1.55 1.56 1.57 1.58 1.59 1.60 1.61 1.62 1.63 1.64 1.65 1.66 1.67 1.68 1.69 1.70 1.71 1.72 1.73 1.74 1.75 1.76 1.77 1.78 1.79 0.433 0.434 0.436 0.437 0.438 0.439 0.441 0.442 0.443 0.444 0.445 0.446 0.447 0.448 0.449 0.451 0.452 0.453 0.454 0.454 0.455 0.456 0.457 0.458 0.459 0.460 0.461 0.462 0.462 0.463
Areas under the Normal Curve
The column under A gives the
proportion of the area under the
entire curve that is between z=0
and a positive value of z.
Because the curve is symmetric
about 0, the area betweenz=0 and
a negative value of z can be found
by using the corresponding positive
value of z.
こ
0.499
0.499
0.499
0.499
0.499
0.499
0.499
0.499
0.499
0.499
0.499
0.499
0.499
0.499
0.499
0.499
0.499
0.499
0.499
0.499
0.499
0.499
0.499
0.499
0.499
0.499
0.499
0.499
0.499
0.499
3.30
3.31
3.32
3.33
3.34
3.35
3.36
3.37
3.38
3.39
3.40
3.41
3.42
3.43
3.44
3.45
3.46
3.47
3.48
3.49
3.50
3.51
3.52
3.53
3.54
3.55
3.56
3.57
3.58
3.59
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.482
2.40
0.483
2.41
0.483
2.42
0.483
2.43
0.484
2.44
0.484
2.45
0.485
2.46
2.47
0.485
0.485
2.48
2.49
0.486
0.486 2.50
0.492
0.492
0.492
0.492
0.493
0.493
0.493
0.493
0.493
0.494
0.494
0.494
0.494
0.494
0.494
0.495
0.495
0.495
0.495
0.495
0.495
0.495
0.496
0.496
0.496
0.496
0.496
0.496
0.496
0.496
2.70
2.71
2.72
2.73
2.74
2.75
2.76
2.77
2.78
2.79
2.80
2.81
2.82
2.83
2.84
2.85
2.86
2.87
2.88
2.89
2.90
2.91
2.92
2.93
2.94
2.95
2.96
2.97
2.98
2.99
0.497
3.00
1.80
1.81
1.82
1.83
1.84
1.85
1.86
1.87
1.88
1.89
1.90
1.91
1.92
1.93
1.94
1.95
1.96
1.97
1.98
1.99
2.00
2.01
2.02
2.03
2.04
2.05
2.06
2.07
2.08
2.09
0.464
0.465
0.466
0.466
0.467
0.468
0.469
0.469
0.470
0.471
0.471
0.472
0.473
0.473
0.474
0.474
0.475
0.476
0.476
0.477
0.477
0.478
0.478
0.479
0.479
0.480
0.480
0.481
0.481
0.482
2.10
2.11
2.12
2.13
2.14
2.15
2.16
2.17
2.18
2.19
2.20
2.21
2.22
2.23
2.24
2.25
2.26
2.27
2.28
2.29
2.30
2.31
2.32
2.33
2.34
2.35
2.36
2.37
2.38
2.39
0.497
3.01
0.497
3.02
0.497
3.03
0.497
3.04
0.497
3.05
0.497
3.06
0.497
3.07
0.497
3.08
0.497
3.09
0.497
3.10
3.11
0.498
3.12
0.498
0.498
3.13
0.498
3.14
3.15
0.498
0.498
3.16
0.498
3.17
3.18
0.498
0.498
3.19
0.498
3.20
0.498
3.21
0.498
3.22
0.498
3.23
0.498
3.24
0.498
3.25
0.498
3.26
0.499
3.27
0.499
3.28
0.499 3.29
0.486
2.51
0.487
2.52
0.487
2.53
0.487
0.488
2.54
2.55
0.488
2.56
0.488
0.489
0.489
0.489
2.57
2.58
2.59
2.60
0.490
2.61
0.490
0.490
0.490
0.491
0.491
2.62
2.63
2.64
2.65
2.66
0.491
2.67
0.491
0.492
2.68
2.69
Transcribed Image Text:Areas under the Normal Curve The column under A gives the proportion of the area under the entire curve that is between z=0 and a positive value of z. Because the curve is symmetric about 0, the area betweenz=0 and a negative value of z can be found by using the corresponding positive value of z. こ 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 0.499 3.30 3.31 3.32 3.33 3.34 3.35 3.36 3.37 3.38 3.39 3.40 3.41 3.42 3.43 3.44 3.45 3.46 3.47 3.48 3.49 3.50 3.51 3.52 3.53 3.54 3.55 3.56 3.57 3.58 3.59 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.482 2.40 0.483 2.41 0.483 2.42 0.483 2.43 0.484 2.44 0.484 2.45 0.485 2.46 2.47 0.485 0.485 2.48 2.49 0.486 0.486 2.50 0.492 0.492 0.492 0.492 0.493 0.493 0.493 0.493 0.493 0.494 0.494 0.494 0.494 0.494 0.494 0.495 0.495 0.495 0.495 0.495 0.495 0.495 0.496 0.496 0.496 0.496 0.496 0.496 0.496 0.496 2.70 2.71 2.72 2.73 2.74 2.75 2.76 2.77 2.78 2.79 2.80 2.81 2.82 2.83 2.84 2.85 2.86 2.87 2.88 2.89 2.90 2.91 2.92 2.93 2.94 2.95 2.96 2.97 2.98 2.99 0.497 3.00 1.80 1.81 1.82 1.83 1.84 1.85 1.86 1.87 1.88 1.89 1.90 1.91 1.92 1.93 1.94 1.95 1.96 1.97 1.98 1.99 2.00 2.01 2.02 2.03 2.04 2.05 2.06 2.07 2.08 2.09 0.464 0.465 0.466 0.466 0.467 0.468 0.469 0.469 0.470 0.471 0.471 0.472 0.473 0.473 0.474 0.474 0.475 0.476 0.476 0.477 0.477 0.478 0.478 0.479 0.479 0.480 0.480 0.481 0.481 0.482 2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18 2.19 2.20 2.21 2.22 2.23 2.24 2.25 2.26 2.27 2.28 2.29 2.30 2.31 2.32 2.33 2.34 2.35 2.36 2.37 2.38 2.39 0.497 3.01 0.497 3.02 0.497 3.03 0.497 3.04 0.497 3.05 0.497 3.06 0.497 3.07 0.497 3.08 0.497 3.09 0.497 3.10 3.11 0.498 3.12 0.498 0.498 3.13 0.498 3.14 3.15 0.498 0.498 3.16 0.498 3.17 3.18 0.498 0.498 3.19 0.498 3.20 0.498 3.21 0.498 3.22 0.498 3.23 0.498 3.24 0.498 3.25 0.498 3.26 0.499 3.27 0.499 3.28 0.499 3.29 0.486 2.51 0.487 2.52 0.487 2.53 0.487 0.488 2.54 2.55 0.488 2.56 0.488 0.489 0.489 0.489 2.57 2.58 2.59 2.60 0.490 2.61 0.490 0.490 0.490 0.491 0.491 2.62 2.63 2.64 2.65 2.66 0.491 2.67 0.491 0.492 2.68 2.69
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