The times taken by workers to assemble a certain kind of cell phone are normally distributed with mean 19.5 minutes and a standard deviation 3.8 minutes. Find the probability that one such phone will require less than 15.7 minutes in assembly The probability that a phone will require less than 15.7 minutes in assembly is ( Round to
The times taken by workers to assemble a certain kind of cell phone are normally distributed with mean 19.5 minutes and a standard deviation 3.8 minutes. Find the probability that one such phone will require less than 15.7 minutes in assembly The probability that a phone will require less than 15.7 minutes in assembly is ( Round to
The times taken by workers to assemble a certain kind of cell phone are normally distributed with mean 19.5 minutes and a standard deviation 3.8 minutes. Find the probability that one such phone will require less than 15.7 minutes in assembly The probability that a phone will require less than 15.7 minutes in assembly is ( Round to
The times taken by workers to assemble a certain kind of cell phone are normally distributed with mean 19.5 minutes and a standard deviation 3.8 minutes. Find the probability that one such phone will require less than 15.7 minutes in assembly
The probability that a phone will require less than 15.7 minutes in assembly is
( Round to three decimal places as needed.)
Transcribed Image Text:Standard Normal Curve Areas (page 1)
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.
Z
A
z
A
Z
0.00
0.60
0.000 0.30 0.118
0.01 0.004 0.31 0.122 0.61
0.02 0.008 0.32 0.126 0.62
0.03 0.012 0.33
0.129 0.63
0.016 0.34
0.04
0.05
0.020 0.35
0.133 0.64
0.65
0.66
0.137
0.06 0.024 0.36
0.141
0.07 0.028 0.37 0.144
0.08
0.67
0.032 0.38 0.148 0.68
0.036 0.39 0.152 0.69
0.09
0.10
0.155 0.70
0.040
0.40
0.044 0.41
0.159 0.71
0.163 0.72
0.11
0.12 0.048 0.42
0.13
0.14
0.052 0.43
0.166 0.73
0.056 0.44 0.170 0.74
0.15
0.060 0.45
0.174 0.75
0.16
0.064 0.46
0.177 0.76
0.17
0.067 0.47
0.18
0.071
0.48
0.181 0.77
0.78
0.79
0.80
0.184
0.188
0.075 0.49
0.079 0.50
0.191
0.083 0.51
0.195 0.81
0.52
0.087
0.198
0.82
0.83
0.202
0.205
0.84
0.19
0.20
0.21
0.22
0.23 0.091 0.53
0.24 0.095
0.54
0.25 0.099 0.55
0.26 0.103 0.56
0.27 0.106 0.57
0.28
0.110 0.58
0.29
0.114
0.59
0.209
0.85
0.212 0.86
0.216 0.87
0.88
0.219
0.222 0.89
0 Z
Z
0.226
0.90
0.229 0.91
0.232 0.92
0.236 0.93
0.239 0.94
0.242 0.95
0.245 0.96
0.249 0.97
0.252 0.98
0.255 0.99
0.258 1.00
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
A
A
A
0.316
0.319
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.
Z
1.20
1.21
0.321
1.22
0.324
1.23
0.326 1.24
0.329 1.25
0.331 1.26
0.334 1.27
0.336 1.28
0.339 1.29
0.341 1.30
0.344
0.346
1.31
1.32
0.348 1.33
0.351 1.34
0.353 1.35
0.355 1.36
0.358 1.37
0.360 1.38
1.39
0.364 1.40
0.367 1.41
0.369
1.42
0.371 1.43
0.373 1.44
0.375
1.45
0.377
1.46
0.379
1.47
0.381 1.48
0.383 1.49
0.285 1.09 0.3
0.288 1.10
0.291 1.11
0.294 1.12
0.297 1.13
0.300 1.14
0.302 1.15
0.305 1.16
0.308 1.17
0.311 1.18
0.313
1.19
A
z
0.385 1.50
0.387 1.51
0.389
1.52
0.391 1.53
0.393
0.394
1.55
0.396
1.56
0.398 1.57
0.400
1.58
0.401 1.59
0.403 1.60
0.405 1.61
0.407 1.62
0.408 1.63
0.410 1.64
0.411 1.65
0.413 1.66
0.415 1.67
0.416 1.68
0.418 1.69
0.419 1.70
0.421
1.71
0.422
1.72
0.424 1.73
0.425
1.74
0.426
1.75
0.428 1.76
0.429
1.77
0.431
1.78
0.432
1.79
A
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
I
Transcribed Image Text:Standard Normal Curve Areas (page 2)
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.
NF
Z
N2
N~
A
A
A
Z
A
Z
1.80 0.464
2.10
0.492
2.70
3.00
3.30
0.497
0.497 3.01
0.499
0.499 3.31
1.81 0.465 2.11
1.82 0.466 2.12
0.499 3.32
0.499 3.33
3.34
0.482 2.40
0.483 2.41 0.492 2.71
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
1.84 0.467 2.14 0.484 2.44 0.493 2.74 0.497 3.04 0.499
1.85 0.468 2.15
0.484 2.45 0.493
2.75
0.497 3.05 0.499
1.86 0.469 2.16 0.485 2.46 0.493 2.76 0.497 3.06
1.87
0.469 2.17 0.485 2.47
1.88 0.470 2.18
1.89 0.471 2.19
3.35
0.499 3.36
3.07 0.499 3.37
0.485 2.48
3.08 0.499
3.38
0.499
3.39
0.493 2.77 0.497
0.497
0.497
3.09
0.497 3.10
0.498 3.11
0.498 3.12
0.499
0.486 2.49
1.90 0.471 2.20 0.486 2.50
1.91 0.472 2.21 0.486 2.51
1.92 0.473 2.22 0.487 2.52
0.473 2.23 0.487 2.53
3.40
0.499 3.41
0.499 3.42
0.499 3.43
1.93
0.498 3.13
1.94
0.474 2.24
0.487 2.54
0.499 3.44
0.499
1.95
0.474 2.25
0.488 2.55
3.45
0.498 3.14
0.498 3.15
0.498 3.16
0.498 3.17
1.96
0.475 2.26
0.488 2.56
0.499 3.46
0.488 2.57
0.499 3.47
0.489 2.58
0.499 3.48
0.476
1.97
2.27
1.98 0.476 2.28
1.99
2.00 0.477 2.30
2.01 0.478 2.31
0.477 2.29
0.489 2.59
0.489 2.60
0.498 3.18
0.498 3.19 0.499 3.49
0.498 3.20 0.499 3.50
0.498 3.21 0.499
0.498 3.22 0.499
0.490 2.61
3.51
2.02
0.478
2.32
0.490
2.62
3.52
2.03
0.479
2.33
0.490 2.63
0.498 3.23
3.53
0.499
0.499
3.24
2.04
0.479
2.34
0.490
2.64
0.498
3.54
2.05
0.480
2.35
0.498
0.499
3.25
2.06
0.480
2.36
0.498
3.26
0.499
2.07
0.481 2.37
0.499
3.27
0.499
2.08 0.481 2.38
0.499
3.28
0.499
2.09
0.482 2.39
0.499
3.29
0.499
0 Z
0.491 2.65
0.491 2.66
0.491 2.67
0.491
2.68
0.492
2.69
22
0.493 2.78
0.494 2.79
0.494 2.80
0.494 2.81
0.494 2.82
0.494 2.83
0.494 2.84
0.495 2.85
0.495 2.86
0.495 2.87
0.495
2.88
0.495 2.89
0.495 2.90
0.495
0.496
0.496
0.496
А
2.91
2.92
2.93
2.94
0.496
2.95
0.496
2.96
0.496
2.97
0.496
2.98
0.496 2.99
AO
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.
3.55
3.56
3.57
3.58
3.59
A
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
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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