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

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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Related questions
Question

A fruit-packing company produced peaches last summer whose weights were normally distributed with mean 16 ounces and standard deviation 0.6 ounces. Among a sample of 1,000 of those peaches, about how many could be expected to have wights between 15.5 and 17.5 ounces?

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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