Задачи 12.1 – 12.30: для нормально распределенной случайной величины X известны математическое ожидание а и среднее квадратическое отклонение σ. Найти:
а) вероятность того, что случайная величина X примет значение. принадлежащее интервалу (α. β);
б) вероятность того, что абсолютная величина разности X-а окажется меньше δ.
| а
| σ
| α
| β
| δ
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12.1
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12.2
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12.3
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12.4
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12.5
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12.6
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12.7
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12.8
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12.9
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12.10
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12.11
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12.12
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12.13
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12.14
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12.15
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12.16
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12.17
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12.18
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12.19
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12.20
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12.21
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12.22
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12.23
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12.24
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12.25
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12.26
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12.27
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12.28
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12.29
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12.30
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III ПРИЛОЖЕНИЯ
Приложение 1
Таблица значений функции 
x
| Ф(x)
| x
| Ф(x)
| x
| Ф(x)
| x
| Ф(x)
| x
| Ф(x)
| x
| Ф(x)
|
0.00
| 0.0000
| 0.50
| 0.1915
| 1.00
| 0.3413
| 1.50
| 0.4332
| 2.00
| 0.4772
| 3.00
| 0.49865
|
0.01
| 0.0040
| 0.51
| 0.1950
| 1.01
| 0.3438
| 1.51
| 0.4345
| 2.02
| 0.4783
| 3.20
| 0.49931
|
0.02
| 0.0080
| 0.52
| 0.1985
| 1.02
| 0.3461
| 1.52
| 0.4357
| 2.04
| 0.4793
| 3.40
| 0.49966
|
0.03
| 0.0120
| 0.53
| 0.2019
| 1.03
| 0.3485
| 1.53
| 0.4370
| 2.06
| 0.4803
| 3.60
| 0.499841
|
0.04
| 0.0160
| 0.54
| 0.2054
| 1.04
| 0.3508
| 1.54
| 0.4382
| 2.08
| 0.4812
| 3.80
| 0.499928
|
0.05
| 0.0199
| 0.55
| 0.2088
| 1.05
| 0.3531
| 1.55
| 0.4394
| 2.10
| 0.4821
| 4.00
| 0.499968
|
0.06
| 0.0239
| 0.56
| 0.2123
| 1.06
| 0.3554
| 1.56
| 0.4406
| 2.12
| 0.4830
| 4.50
| 0.499997
|
0.07
| 0.0279
| 0.57
| 0.2157
| 1.07
| 0.3577
| 1.57
| 0.4418
| 2.14
| 0.4838
| 5.00
| 0.499997
|
0.08
| 0.0319
| 0.58
| 0.2190
| 1.08
| 0.3599
| 1.58
| 0.4429
| 2.16
| 0.4846
|
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0.09
| 0.0359
| 0.59
| 0.2224
| 1.09
| 0.3621
| 1.59
| 0.4441
| 2.18
| 0.4854
|
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|
0.10
| 0.0398
| 0.60
| 0.2257
| 1.10
| 0.3643
| 1.60
| 0.4452
| 2.20
| 0.4861
|
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0.11
| 0.0438
| 0.61
| 0.2291
| 1.11
| 0.3665
| 1.61
| 0.4463
| 2.22
| 0.4868
|
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0.12
| 0.0478
| 0.62
| 0.2324
| 1.12
| 0.3686
| 1.62
| 0.4474
| 2.24
| 0.4875
|
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|
0.13
| 0.0517
| 0.63
| 0.2357
| 1.13
| 0.3708
| 1.63
| 0.4484
| 2.26
| 0.4881
|
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0.14
| 0.0557
| 0.64
| 0.2389
| 1.14
| 0.3729
| 1.64
| 0.4495
| 2.28
| 0.4887
|
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0.15
| 0.0596
| 0.65
| 0.2422
| 1.15
| 0.3749
| 1.65
| 0.4505
| 2.30
| 0.4893
|
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0.16
| 0.0636
| 0.66
| 0.2454
| 1.16
| 0.3770
| 1.66
| 0.4515
| 2.32
| 0.4898
|
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0.17
| 0.0675
| 0.67
| 0.2486
| 1.17
| 0.3790
| 1.67
| 0.4525
| 2.34
| 0.4904
|
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0.18
| 0.0714
| 0.68
| 0.2517
| 1.18
| 0.3810
| 1.68
| 0.4535
| 2.36
| 0.4909
|
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0.19
| 0.0753
| 0.69
| 0.2549
| 1.19
| 0.3830
| 1.69
| 0.4545
| 2.38
| 0.4913
|
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0.20
| 0.0793
| 0.70
| 0.2580
| 1.20
| 0.3849
| 1.70
| 0.4554
| 2.40
| 0.4918
|
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0.21
| 0.0832
| 0.71
| 0.2611
| 1.21
| 0.3869
| 1.71
| 0.4564
| 2.42
| 0.4922
|
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0.22
| 0.0871
| 0.72
| 0.2642
| 1.22
| 0.3883
| 1.72
| 0.4573
| 2.44
| 0.4927
|
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0.23
| 0.0910
| 0.73
| 0.2673
| 1.23
| 0.3907
| 1.73
| 0.4582
| 2.46
| 0.4931
|
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0.24
| 0.0948
| 0.74
| 0.2703
| 1.24
| 0.3925
| 1.74
| 0.4591
| 2.48
| 0.4934
|
|
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0.25
| 0.0987
| 0.75
| 0.2734
| 1.25
| 0.3944
| 1.75
| 0.4599
| 2.50
| 0.4938
|
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0.26
| 0.1026
| 0.76
| 0.2764
| 1.26
| 0.3962
| 1.76
| 0.4608
| 2.52
| 0.4941
|
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0.27
| 0.1064
| 0.77
| 0.2794
| 1.27
| 0.3980
| 1.77
| 0.4616
| 2.54
| 0.4945
|
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0.28
| 0.1103
| 0.78
| 0.2823
| 1.28
| 0.3997
| 1.78
| 0.4625
| 2.56
| 0.4948
|
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0.29
| 0.1141
| 0.79
| 0.2852
| 1.29
| 0.4015
| 1.79
| 0.4633
| 2.58
| 0.4951
|
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0.30
| 0.1179
| 0.80
| 0.2881
| 1.30
| 0.4032
| 1.80
| 0.4641
| 2.60
| 0.4953
|
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0.31
| 0.1217
| 0.81
| 0.2910
| 1.31
| 0.4049
| 1.81
| 0.4649
| 2.62
| 0.4956
|
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0.32
| 0.1255
| 0.82
| 0.2939
| 1.32
| 0.4066
| 1.82
| 0.4656
| 2.64
| 0.4959
|
|
|
0.33
| 0.1293
| 0.83
| 0.2967
| 1.33
| 0.4082
| 1.83
| 0.4664
| 2.66
| 0.4961
|
|
|
0.34
| 0.1331
| 0.84
| 0.2995
| 1.34
| 0.4099
| 1.84
| 0.4671
| 2.68
| 0.4963
|
|
|
0.35
| 0.1368
| 0.85
| 0.3023
| 1.35
| 0.4115
| 1.85
| 0.4678
| 2.70
| 0.4965
|
|
|
0.36
| 0.1406
| 0.86
| 0.3051
| 1.36
| 0.4131
| 1.86
| 0.4686
| 2.72
| 0.4967
|
|
|
0.37
| 0.1443
| 0.87
| 0.3078
| 1.37
| 0.4147
| 1.87
| 0.4693
| 2.74
| 0.4969
|
|
|
0.38
| 0.1480
| 0.88
| 0.3106
| 1.38
| 0.4162
| 1.88
| 0.4699
| 2.76
| 0.4971
|
|
|
0.39
| 0.1517
| 0.89
| 0.3133
| 1.39
| 0.4177
| 1.89
| 0.4706
| 2.78
| 0.4973
|
|
|
0.40
| 0.1554
| 0.90
| 0.3159
| 1.40
| 0.4192
| 1.90
| 0.4713
| 2.80
| 0.4974
|
|
|
0.41
| 0.1591
| 0.91
| 0.3186
| 1.41
| 0.4207
| 1.91
| 0.4719
| 2.82
| 0.4976
|
|
|
0.42
| 0.1628
| 0.92
| 0.3212
| 1.42
| 0.4222
| 1.92
| 0.4726
| 2.84
| 0.4977
|
|
|
0.43
| 0.1664
| 0.93
| 0.3238
| 1.43
| 0.4236
| 1.93
| 0.4732
| 2.86
| 0.4979
|
|
|
0.44
| 0.1700
| 0.94
| 0.3264
| 1.44
| 0.4251
| 1.94
| 0.4738
| 2.88
| 0.4980
|
|
|
0.45
| 0.1736
| 0.95
| 0.3289
| 1.45
| 0.4265
| 1.95
| 0.4744
| 2.90
| 0.4981
|
|
|
0.46
| 0.1772
| 0.96
| 0.3315
| 1.46
| 0.4279
| 1.96
| 0.4750
| 2.92
| 0.4982
|
|
|
0.47
| 0.1808
| 0.97
| 0.3340
| 1.47
| 0.4292
| 1.97
| 0.4756
| 2.94
| 0.4984
|
|
|
0.48
| 0.1844
| 0.98
| 0.3365
| 1.48
| 0.4306
| 1.98
| 0.4761
| 2.96
| 0.4985
|
|
|
0.49
| 0.1879
| 0.99
| 0.3389
| 1.49
| 0.4319
| 1.99
| 0.4767
| 2.98
| 0.4986
|
|
|