I could use some statistic assistance in the following: Find the value of z such that 75.2% of the total area is to the left of z. z= ___________
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!
I could use some statistic assistance in the following:
Find the value of z such that 75.2% of the total area is to the left of z.
z= ___________
(Round to two decimal places as needed.)
Note: the standard curve is for reference only.
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the area under the entire curve that is
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.000
.56
.212
1.12
.369
1.68
.454
2.24
487
2.80
.497
between z= 0 and a positive value of z.
.01
.004
.57
.216
1.13
.371
1.69
454
2.25
.488
2.81
498
.02
.008
.58
219
1.14
.373
1.70
455
2.26
.488
2.82
498
.03
.012
.59
.222
1.15
.375
1.71
456
2.27
.488
2.83
.498
.04
.016
60
.226
1.16
.377
1.72
.457
2.28
.489
2.84
.498
.05
.020
.61
.229
1.17
.379
1.73
.458
2.29
.489
2.85
498
.024
.028
.06
.62
232
1.18
.381
1.74
.459
2.30
.489
2.86
498
.07
.63
236
1.19
.383
1.75
460
2.31
.490
2.87
.498
.08
.032
64
.239
1.20
385
1.76
461
2.32
.490
2.88
498
Because the curve is symmetric about the
.09
.036
65
.242
1.21
387
1.77
462
2.33
.490
2.89
498
0-value, the area between z= 0 and a
.10
.040
.66
245
1.22
.389
1.78
.462
2.34
.490
2.90
498
negative value of z can be found by using
.11
.044
.67
.249
1.23
.391
1.79
.463
2.35
.491
2.91
.498
the corresponding positive value of z.
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2.92
2.93
.12
.048
.68
.252
.393
1.80
.464
2.36
491
498
.13
.052
69
.255
1.25
.394
1.81
465
2.37
.491
.498
.14
.056
.70
.258
1.26
396
1.82
466
2.38
.491
2.94
.498
.15
.060
.71
.261
1.27
.398
1.83
466
2.39
.492
2.95
498
498
499
.499
.499
.16
.064
.72
264
1.28
.400
1.84
467
2.40
.492
2.96
2.97
2.98
.17
.067
.73
.267
1.29
.401
1.85
468
2.41
.492
.18
.071
.74
.270
1.30
.403
1.86
.469
2.42
.492
.19
.075
.75
273
1.31
.405
1.87
.469
2.43
492
2.99
20
.079
76
276
1.32
.407
1.88
.470
2.44
.493
3.00
499
.21
.083
.77
.279
1.33
.408
1.89
.471
2.45
.493
3.01
499
.22
.087
.78
.282
1.34
.410
1.90
471
2.46
493
3.02
.499
.23
.091
.79
.285
1.35
411
1.91
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2.47
493
3.03
499
.288
.291
24
.095
.80
1.36
.413
1.92
.473
2.48
493
3.04
499
.25
.099
.81
1.37
.415
1.93
.473
2.49
.494
3.05
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499
.499
.26
.103
82
.294
1.38
.416
1.94
.474
2.50
.494
3.06
.27
.106
83
.297
1.39
.418
1.95
.474
2.51
.494
3.07
28
.110
.84
.300
1.40
.419
1.96
.475
2.52
494
3.08
499
.29
.114
.85
.302
1.41
.421
1.97
476
2.53
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3.09
.499
.30
.118
.86
.305
1.42
422
1.98
476
2.54
.494
3.10
499
31
.122
.87
.308
1.43
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1.99
477
2.55
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3.11
499
32
.126
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.311
1.44
.425
2.00
.477
2.56
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3.12
499
33
.129
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.313
1.45
426
2.01
478
2.57
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3.13
499
.478
.479
.34
.133
.90
.316
1.46
.428
2.02
2.58
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3.14
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.35
.137
.91
.319
1.47
.429
2.03
2.59
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3.15
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36
.141
.92
.321
1.48
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2.04
479
2.60
495
3.16
499
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.37
.144
93
.324
1.49
432
2.05
480
2.61
495
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.148
94
.326
1.50
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2.06
480
2.62
.496
3.18
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152
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.329
1.51
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2.07
481
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3.19
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.40
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.331
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1.52
1.53
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.481
2.64
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3.20
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.41
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.334
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2.09
482
2.65
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3.21
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42
.163
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.336
1.54
438
2.10
482
2.66
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3.22
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43
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1.55
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2.11
483
2.67
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3.23
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3.24
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1.00
.341
1.56
441
2.12
.483
2.68
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45
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1.01
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2.13
483
2.69
.496
499
46
177
1.02
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1.58
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2.14
.484
2.70
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3.26
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47
.181
1.03
.348
1.59
.444
2.15
484
2.71
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3.27
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48
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1.04
.351
1.60
445
2.16
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2.72
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3.28
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2.17
2.18
49
.188
1.05
.353
1.61
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.485
2.73
.497
3.29
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50
191
1.06
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485
2.74
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3.30
500
51
.195
1.07
.358
1.63
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2.19
486
2.75
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3.31
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.486
.486
3.32
3,33
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.198
1.08
.360
1.64
.449
2.20
2.76
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.500
.53
.202
1.09
.362
1.65
.451
2.21
2.77
.497
.500
.54
.205
1.10
.364
1.66
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2.22
487
2.78
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3.34
.500
.55
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1.67
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2.23
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2.79
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3.35
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