A fruit-packing company produced peaches last summer whose weights were normally distributed with mean 12 ounces and standard deviation 0.8 ounce. Among a sample of 1000 of those peaches, about how many could be expected to have weights between 11.3 and 13.2 ounces? The number of peaches expected to have weights between 11.3 and 13.2 ounces is _______
A fruit-packing company produced peaches last summer whose weights were normally distributed with mean 12 ounces and standard deviation 0.8 ounce. Among a sample of 1000 of those peaches, about how many could be expected to have weights between 11.3 and 13.2 ounces? The number of peaches expected to have weights between 11.3 and 13.2 ounces is _______
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Question
100%
A fruit-packing company produced peaches last summer whose weights were
The number of peaches expected to have weights between 11.3 and 13.2 ounces is _______
(NOTE: Round to the nearest whole number)
Transcribed Image Text: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.
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.
A
0.497
0.497
0.497
0.497
0.497
0.497
0.497
0.497
0.497
0.497
0.497
A
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
A
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
A
Iz
0.482
2.40
0.483
2.41
2.42
0.483
2.43
0.483
2.44
0.484
2.45
0.484
2.46
0.485
0.485
2.47
2.48
0.485
2.49
0.486
0.486
2.50
2.51
0.486
0.487
2.52
2.53
0.487
2.54
0.487
0.488
2.55
2.56
0.488
2.57
0.488
2.58
0.489
0.489
2.59
0.489
2.60
0.490
2.61
2.62
0.490
0.490
2.63
2.64
0.490
0.491
2.65
0.491
2.66
0.491
2.67
0.491
2.68
2.69
0.492
3.00
3.01
3.02
3.03
3.04
3.05
3.06
3.07
3.08
3.09
3.10
3.11
3.12
3.13
3.14
3.15
3.16
3.17
3.18
3.19
3.20
3.21
3.22
3.23
3.24
3.25
3.26
3.27
3.28
3.29
2.70
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
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
1.80
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
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
1.81
2.71
1.82
1.83
1.84
1.85
1.86
1.87
1.88
1.89
1.90
2.72
2.73
2.74
2.75
2.76
2.77
2.78
2.79
2.80
1.91
2.81
0.498
2.82
2.83
1.92
1.93
1.94
1.95
1.96
1.97
1.98
1.99
2.00
0.498
0.498
2.84
0.498
2.85
0.498
2.86
0.498
2.87
2.88
2.89
2.90
0.498
0.498
0.498
0.498
2.01
2.91
0.498
2.02
2.03
2.04
2.05
2.06
2.07
2.08
2.09
2.92
2.93
2.94
2.95
2.96
0.498
0.498
0.498
0.498
0.498
2.97
0.499
2.98
2.99
0.499
0.499
Transcribed Image Text: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.
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.
A
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
A
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
A
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
A
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
A
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
0.00
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
1.20
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
0.90
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
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
0.01
0.91
1.21
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
0.92
0.93
0.94
0.95
0.96
0.97
0.98
0.99
1.00
1.22
1.23
1.24
1.25
1.26
1.27
1.28
1.29
1.30
0.11
1.01
1.31
0.12
0.13
0.14
0.15
0.16
0.17
0.18
0.19
0.20
1.02
1.03
1.04
1.05
1.06
1.07
1.08
1.09
1.10
1.32
1.33
1.34
1.35
1.36
1.37
1.38
1.39
1.40
0.21
1.11
1.41
0.22
0.23
0.24
0.25
0.26
0.27
0.28
0.29
1.12
1.13
1.14
1.15
1.16
1.17
1.18
1.19
1.42
1.43
1.44
1.45
1.46
1.47
1.48
1.49
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