In nutrition, the recommended daily allowance of vitamins is a number set by the government to guide an individual's daily vitamin intake. Actually, vitamin needs vary drastically from person to person, but the needs are closely approximated by a normal curve. To calculate the recommended daily allowance, the government first finds the standard deviation and the average need for vitamins among people in the population. The recommended daily allowance is then defined as the mean plus 2.3 times the standard deviation. What fraction of the population will receive adequate amounts of vitamins under this plan? Click here to see page 1 of the table for areas under the standard normal curve. Click here to see page 2 of the table for areas under the standard normal curve. The fraction of the population that will receive adequate amounts of vitamins under the given plan is (Type an integer or decimal rounded to the nearest thousandth as needed.)
In nutrition, the recommended daily allowance of vitamins is a number set by the government to guide an individual's daily vitamin intake. Actually, vitamin needs vary drastically from person to person, but the needs are closely approximated by a normal curve. To calculate the recommended daily allowance, the government first finds the standard deviation and the average need for vitamins among people in the population. The recommended daily allowance is then defined as the mean plus 2.3 times the standard deviation. What fraction of the population will receive adequate amounts of vitamins under this plan? Click here to see page 1 of the table for areas under the standard normal curve. Click here to see page 2 of the table for areas under the standard normal curve. The fraction of the population that will receive adequate amounts of vitamins under the given plan is (Type an integer or decimal rounded to the nearest thousandth as needed.)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Transcribed Image Text:In nutrition, the recommended daily allowance of vitamins is a number set by the government to guide an individual's daily vitamin intake. Actually, vitamin needs vary drastically from person
to person, but the needs are closely approximated by a normal curve. To calculate the recommended daily allowance, the government first finds the standard deviation and the average need for
vitamins among people in the population. The recommended daily allowance is then defined as the mean plus 2.3 times the standard deviation. What fraction of the population will receive adequate
amounts of vitamins under this plan?
Click here to see page 1 of the table for areas under the standard normal curve.
Click here to see page 2 of the table for areas under the standard normal curve.
The fraction of the population that will receive adequate amounts of vitamins under the given plan is
(Type an integer or decimal rounded to the nearest thousandth as needed.)
Transcribed Image Text:Standard Normal Curve Areas (page 1)
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.
z
0.00
A
Z
A
Z
0 2
A
z
0.000 0.30 0.118 0.60 0.226 0.90
0.01 0.004 0.31 0.122 0.61 0.229
0.02 0.008 0.32 0.126 0.62 0.232
0.03 0.012 0.33 0.129 0.63 0.236 0.93
0.04 0.016 0.34
0.05 0.020 0.35
0.06 0.024 0.36
0.07 0.028 0.37
0.08 0.032 0.38 0.148 0.68
0.09 0.036 0.39 0.152 0.69
0.10 0.040 0.40
0.155 0.70
0.239
0.133 0.64
0.137
0.94
0.95
0.65
0.242
0.141
0.66
0.245
0.96
0.144
0.67
0.249 0.97
0.11 0.044 0.41 0.159 0.71
0.12 0.048 0.42 0.163 0.72
0.13 0.052 0.43 0.166 0.73
0.14 0.056 0.44 0.170 0.74
0.15 0.060 0.45 0.174 0.75
0.16 0.064
0.177
0.46
0.76
0.17
0.47
0.067
0.181 0.77
0.071 0.48 0.184 0.78
0.252
0.98
0.255 0.99 0.339
0.258 1.00 0.341
0.261 1.01
0.264 1.02
0.267 1.03
0.270 1.04
0.273 1.05
0.276 1.06
0.279 1.07
0.282 1.08
0.075
0.49
0.188
0.79
0.285 1.09
0.079
0.191
0.80
0.288
1.10
0.083
0.81
0.195
0.291
1.11
0.087
0.198 0.82
0.294
0.091
0.83
0.297
0.095
0.84
0.300
0.25
0.099
0.85
0.302
0.26
0.103
0.86
0.305
0.27
0.106
0.28 0.110
0.29
0.18
0.19
0.20
0.21
0.22
0.23
0.24
0.114 0.59
1.90
0.471
1.91 0.472
1.92
1.93
0.50
0.51
0.52
0.53
0.202
0.54 0.205
0,209
0.212
0.216
1.94
1.95
1.96
1.97
1.98
1.99
0.55
0.56
0.57
0.58
0.473
0.473
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.
Areas under the Normal Curve
0.219
0.222
Standard Normal Curve Areas (page 2)
0.475
0.476
0.477 2.29
2.00
0.477
2.30
2.01
0.478
2.02
0.478
2.03
0.479
2.04
0.479
2.05
0.480
2.06
0.480
2.07 0.481
2.08
0.481
2.09
0.482 2.39
0.488
2.26
2.27
0.488
2.28
0.476
0.489
0.489
0.489
2.31 0.490
2.32
0.490
0.87 0.308
0.88
0.311
0.89
0.313 1.19
A
0.316
0.91 0.319
0.92 0.321 1.22
0.324 1.23
0.326 1.24
0.329 1.25
0.331 1.26 0.396
0.334 1.27
0.398
0.336 1.28 0.400
1.12
1.13
1.14
1.15
1.16
1.17
1.18
0.490
2.33
2.34
0.490
2.35
0.491
2.36
0.491
2.37 0.491
0.491
2.38
Areas under the Normal Curve
s
0
2
0.496
0.496
0.496
Because the curve is symmetric
about 0, the area between z = 0
and a negative value of z can be
found by using the corresponding
positive value of z.
A
z
0.385 1.50
1.21 0.387 1.51
0.389
1.52
0.391 1.53
0.355
0.358
0.360
0.362
0.364
0.367
0.369
0.371
0.373
0.375 1.45
z
1.20
2.84
2.85 0.498
2.86
2.87
2.88
2.89
2.90
2.91
2.92
1.29 0.401 1.59
1.30 0.403 1.60
0.344 1.31 0.405 1.61
0.346 1.32 0.407 1.62
0.348 1.33 0.408 1.63
0.351 1.34 0.410 1.64
0.353 1.35 0.411 1.65
0.413
1.66
1.67
0.415
1.68
1.69
1.70
1.71
1.72
1.73
0.377
1.46
0.379
1.47
0.381
1.48
0.383 1.49
0.498
0.498
2.93
0.498
2.94 0.498
1.36
1.37
1.38
0.416
0.418
1.39
1.40
0.419
1.41
0.421
1.42
0.422
1.43
0.424
1.44 0.425
0.426
0.428
Z
Z
Z
Z
A
z
z
A
A
0.499 3.30
0.500
0.499 3.31
0.500
0.499 3.32
0.500
0.500
A
A
A
1.80 0.464 2.10 0.482 2.40 0.492 2.70 0.497 3.00
1.81 0.465 2.11 0.483 2.41 0.492 2.71 0.497 3.01
1.82 0.466 2.12 0.483 2.42 0.492 2.72 0.497 3.02
1.83 0.466 2.13 0.483 2.43 0.492 2.73 0.497 3.03 0.499 3.33
1.84 0.467 2.14 0.484 2.44 0.493 2.74 0.497 3.04 0.499 3.34 0.500
0.484 2.45 0.493 2.75 0.497 3.05 0.499 3.35 0.500
0.485 2.46 0.493 2.76 0.497 3.06 0.499 3.36 0.500
0.485 2.47 0.493 2.77 0.497 3.07 0.499 3.37
0.499 3.38
1.85 0.468 2.15
1.86 0.469 2.16
1.87 0.469 2.17
1.88 0.470 2.18
0.500
0.485
2.48
0.500
0.493 2.78
0.494 2.79
0.497 3.08
0.497
1.89 0.471 2.19
0.486
2.49
3.09 0.499
3.39 0.500
2.20
0.486
2.50
0.494 2.80
0.497
3.10
0.499 3.40
0.500
2.21
0.486
2.51
0.494 2.81
0.498
3.11
0.499
3.41
0.500
2.22
0.487
2.52
0.494 2.82
0.498
3.12 0.499
3.42
0.500
2.23 0.487 2.53
0.494
2.83
0.498 3.13
0.499
3.43
0.500
2.54
0.474
0.494
2.24
0.498
3.44
3.14
0.499
0.500
0.487
0.488 2.55
0.474 2.25
0.495
3.45
3.15 0.499
2.56 0.495
3.46
2.57
0.495
3.47
2.58
0.495
2.59 0.495
2.60
0.495
2.61
0.495
2.62
2.63
2.64
2.65
2.66
2.67
2.68
2.69
0.492
0.393 1.54
0.394
0.498 3.16
0.498
3.17
0.498
3.18
0.498
3.19
0.498
3.20
3.21
3.22
1.55
1.56
1.57
1.58
1.76
0.429
1.77
0.431 1.78
0.432
1.79
0.499
0.499
0.499
1.74
1.75
0.499
0.499
0.496
0.496
3.23
0.496
3.24
0.496 2.95
3.25 0.499
0.498
3.26
0.498
0.496 2.96
0.499
2.97
0.499 3.27 0.499
0.499
3.28
0.499
2.98
2.99 0.499 3.29 0.499
Because the curve is symmetric
about 0, the area between z=0
and a negative value of z can be
found by using the corresponding
positive value of z.
3.48
3.49
3.50
3.51
A
0.433
0.434
0.436
0.437
0.438
0,439
0.441
0.442
0.443
0.444
0.499
0.499
3.52
3.53
0.499
0.499
3.55
3.56
0.445
0.446
0.447
0.448
0.449
0.451
0.452
0.453
0.454
0.454
0.455
0.456
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
3.54 0.500
0.500
3.57
3.58
3.59
0.457
0.458
0.459
0.460
0.461
0.462
0.462
0.463
0.500
0.500
0.500
0.500
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