Verteilungstabellen
Die dargestellten Werte wurden mittels der Statistiksoftware R ausgegeben.
Tabelle 8.1: Verteilungstabelle zur Standardormalverteilung: Die fett dargestellten Werte sind die Ausprägungen der standardnormalverteilten Zufallsvariablen Z; z.B. \(\mathbb P(Z\leq 0.51)=0.6950\)
|
z
|
0.00
|
0.01
|
0.02
|
0.03
|
0.04
|
0.05
|
0.06
|
0.07
|
0.08
|
0.09
|
|
0.0
|
0.5000
|
0.5040
|
0.5080
|
0.5120
|
0.5160
|
0.5199
|
0.5239
|
0.5279
|
0.5319
|
0.5359
|
|
0.1
|
0.5398
|
0.5438
|
0.5478
|
0.5517
|
0.5557
|
0.5596
|
0.5636
|
0.5675
|
0.5714
|
0.5753
|
|
0.2
|
0.5793
|
0.5832
|
0.5871
|
0.5910
|
0.5948
|
0.5987
|
0.6026
|
0.6064
|
0.6103
|
0.6141
|
|
0.3
|
0.6179
|
0.6217
|
0.6255
|
0.6293
|
0.6331
|
0.6368
|
0.6406
|
0.6443
|
0.6480
|
0.6517
|
|
0.4
|
0.6554
|
0.6591
|
0.6628
|
0.6664
|
0.6700
|
0.6736
|
0.6772
|
0.6808
|
0.6844
|
0.6879
|
|
0.5
|
0.6915
|
0.6950
|
0.6985
|
0.7019
|
0.7054
|
0.7088
|
0.7123
|
0.7157
|
0.7190
|
0.7224
|
|
0.6
|
0.7257
|
0.7291
|
0.7324
|
0.7357
|
0.7389
|
0.7422
|
0.7454
|
0.7486
|
0.7517
|
0.7549
|
|
0.7
|
0.7580
|
0.7611
|
0.7642
|
0.7673
|
0.7704
|
0.7734
|
0.7764
|
0.7794
|
0.7823
|
0.7852
|
|
0.8
|
0.7881
|
0.7910
|
0.7939
|
0.7967
|
0.7995
|
0.8023
|
0.8051
|
0.8078
|
0.8106
|
0.8133
|
|
0.9
|
0.8159
|
0.8186
|
0.8212
|
0.8238
|
0.8264
|
0.8289
|
0.8315
|
0.8340
|
0.8365
|
0.8389
|
|
1.0
|
0.8413
|
0.8438
|
0.8461
|
0.8485
|
0.8508
|
0.8531
|
0.8554
|
0.8577
|
0.8599
|
0.8621
|
|
1.1
|
0.8643
|
0.8665
|
0.8686
|
0.8708
|
0.8729
|
0.8749
|
0.8770
|
0.8790
|
0.8810
|
0.8830
|
|
1.2
|
0.8849
|
0.8869
|
0.8888
|
0.8907
|
0.8925
|
0.8944
|
0.8962
|
0.8980
|
0.8997
|
0.9015
|
|
1.3
|
0.9032
|
0.9049
|
0.9066
|
0.9082
|
0.9099
|
0.9115
|
0.9131
|
0.9147
|
0.9162
|
0.9177
|
|
1.4
|
0.9192
|
0.9207
|
0.9222
|
0.9236
|
0.9251
|
0.9265
|
0.9279
|
0.9292
|
0.9306
|
0.9319
|
|
1.5
|
0.9332
|
0.9345
|
0.9357
|
0.9370
|
0.9382
|
0.9394
|
0.9406
|
0.9418
|
0.9429
|
0.9441
|
|
1.6
|
0.9452
|
0.9463
|
0.9474
|
0.9484
|
0.9495
|
0.9505
|
0.9515
|
0.9525
|
0.9535
|
0.9545
|
|
1.7
|
0.9554
|
0.9564
|
0.9573
|
0.9582
|
0.9591
|
0.9599
|
0.9608
|
0.9616
|
0.9625
|
0.9633
|
|
1.8
|
0.9641
|
0.9649
|
0.9656
|
0.9664
|
0.9671
|
0.9678
|
0.9686
|
0.9693
|
0.9699
|
0.9706
|
|
1.9
|
0.9713
|
0.9719
|
0.9726
|
0.9732
|
0.9738
|
0.9744
|
0.9750
|
0.9756
|
0.9761
|
0.9767
|
|
2.0
|
0.9772
|
0.9778
|
0.9783
|
0.9788
|
0.9793
|
0.9798
|
0.9803
|
0.9808
|
0.9812
|
0.9817
|
|
2.1
|
0.9821
|
0.9826
|
0.9830
|
0.9834
|
0.9838
|
0.9842
|
0.9846
|
0.9850
|
0.9854
|
0.9857
|
|
2.2
|
0.9861
|
0.9864
|
0.9868
|
0.9871
|
0.9875
|
0.9878
|
0.9881
|
0.9884
|
0.9887
|
0.9890
|
|
2.3
|
0.9893
|
0.9896
|
0.9898
|
0.9901
|
0.9904
|
0.9906
|
0.9909
|
0.9911
|
0.9913
|
0.9916
|
|
2.4
|
0.9918
|
0.9920
|
0.9922
|
0.9925
|
0.9927
|
0.9929
|
0.9931
|
0.9932
|
0.9934
|
0.9936
|
|
2.5
|
0.9938
|
0.9940
|
0.9941
|
0.9943
|
0.9945
|
0.9946
|
0.9948
|
0.9949
|
0.9951
|
0.9952
|
|
2.6
|
0.9953
|
0.9955
|
0.9956
|
0.9957
|
0.9959
|
0.9960
|
0.9961
|
0.9962
|
0.9963
|
0.9964
|
|
2.7
|
0.9965
|
0.9966
|
0.9967
|
0.9968
|
0.9969
|
0.9970
|
0.9971
|
0.9972
|
0.9973
|
0.9974
|
|
2.8
|
0.9974
|
0.9975
|
0.9976
|
0.9977
|
0.9977
|
0.9978
|
0.9979
|
0.9979
|
0.9980
|
0.9981
|
|
2.9
|
0.9981
|
0.9982
|
0.9982
|
0.9983
|
0.9984
|
0.9984
|
0.9985
|
0.9985
|
0.9986
|
0.9986
|
|
3.0
|
0.9987
|
0.9987
|
0.9987
|
0.9988
|
0.9988
|
0.9989
|
0.9989
|
0.9989
|
0.9990
|
0.9990
|
Tabelle 8.2: Verteilungstabelle zur t-Verteilung: Quantile nach ausgewählten Wahrscheinlichkeiten und Freiheitsgraden
|
|
p=
|
|
\(\nu\)
|
0.6
|
0.75
|
0.9
|
0.95
|
0.975
|
0.99
|
0.995
|
0.999
|
|
1
|
0.325
|
1.000
|
3.078
|
6.314
|
12.706
|
31.821
|
63.657
|
318.309
|
|
2
|
0.289
|
0.816
|
1.886
|
2.920
|
4.303
|
6.965
|
9.925
|
22.327
|
|
3
|
0.277
|
0.765
|
1.638
|
2.353
|
3.182
|
4.541
|
5.841
|
10.215
|
|
4
|
0.271
|
0.741
|
1.533
|
2.132
|
2.776
|
3.747
|
4.604
|
7.173
|
|
5
|
0.267
|
0.727
|
1.476
|
2.015
|
2.571
|
3.365
|
4.032
|
5.893
|
|
6
|
0.265
|
0.718
|
1.440
|
1.943
|
2.447
|
3.143
|
3.707
|
5.208
|
|
7
|
0.263
|
0.711
|
1.415
|
1.895
|
2.365
|
2.998
|
3.499
|
4.785
|
|
8
|
0.262
|
0.706
|
1.397
|
1.860
|
2.306
|
2.896
|
3.355
|
4.501
|
|
9
|
0.261
|
0.703
|
1.383
|
1.833
|
2.262
|
2.821
|
3.250
|
4.297
|
|
10
|
0.260
|
0.700
|
1.372
|
1.812
|
2.228
|
2.764
|
3.169
|
4.144
|
|
11
|
0.260
|
0.697
|
1.363
|
1.796
|
2.201
|
2.718
|
3.106
|
4.025
|
|
12
|
0.259
|
0.695
|
1.356
|
1.782
|
2.179
|
2.681
|
3.055
|
3.930
|
|
13
|
0.259
|
0.694
|
1.350
|
1.771
|
2.160
|
2.650
|
3.012
|
3.852
|
|
14
|
0.258
|
0.692
|
1.345
|
1.761
|
2.145
|
2.624
|
2.977
|
3.787
|
|
15
|
0.258
|
0.691
|
1.341
|
1.753
|
2.131
|
2.602
|
2.947
|
3.733
|
|
16
|
0.258
|
0.690
|
1.337
|
1.746
|
2.120
|
2.583
|
2.921
|
3.686
|
|
17
|
0.257
|
0.689
|
1.333
|
1.740
|
2.110
|
2.567
|
2.898
|
3.646
|
|
18
|
0.257
|
0.688
|
1.330
|
1.734
|
2.101
|
2.552
|
2.878
|
3.610
|
|
19
|
0.257
|
0.688
|
1.328
|
1.729
|
2.093
|
2.539
|
2.861
|
3.579
|
|
20
|
0.257
|
0.687
|
1.325
|
1.725
|
2.086
|
2.528
|
2.845
|
3.552
|
|
21
|
0.257
|
0.686
|
1.323
|
1.721
|
2.080
|
2.518
|
2.831
|
3.527
|
|
22
|
0.256
|
0.686
|
1.321
|
1.717
|
2.074
|
2.508
|
2.819
|
3.505
|
|
23
|
0.256
|
0.685
|
1.319
|
1.714
|
2.069
|
2.500
|
2.807
|
3.485
|
|
24
|
0.256
|
0.685
|
1.318
|
1.711
|
2.064
|
2.492
|
2.797
|
3.467
|
|
25
|
0.256
|
0.684
|
1.316
|
1.708
|
2.060
|
2.485
|
2.787
|
3.450
|
|
26
|
0.256
|
0.684
|
1.315
|
1.706
|
2.056
|
2.479
|
2.779
|
3.435
|
|
27
|
0.256
|
0.684
|
1.314
|
1.703
|
2.052
|
2.473
|
2.771
|
3.421
|
|
28
|
0.256
|
0.683
|
1.313
|
1.701
|
2.048
|
2.467
|
2.763
|
3.408
|
|
29
|
0.256
|
0.683
|
1.311
|
1.699
|
2.045
|
2.462
|
2.756
|
3.396
|
|
30
|
0.256
|
0.683
|
1.310
|
1.697
|
2.042
|
2.457
|
2.750
|
3.385
|
|
40
|
0.255
|
0.681
|
1.303
|
1.684
|
2.021
|
2.423
|
2.704
|
3.307
|
|
60
|
0.254
|
0.679
|
1.296
|
1.671
|
2.000
|
2.390
|
2.660
|
3.232
|
|
80
|
0.254
|
0.678
|
1.292
|
1.664
|
1.990
|
2.374
|
2.639
|
3.195
|
|
100
|
0.254
|
0.677
|
1.290
|
1.660
|
1.984
|
2.364
|
2.626
|
3.174
|
|
1000
|
0.253
|
0.675
|
1.282
|
1.646
|
1.962
|
2.330
|
2.581
|
3.098
|
|
Inf
|
0.253
|
0.674
|
1.282
|
1.645
|
1.960
|
2.326
|
2.576
|
3.090
|
Tabelle 8.3: Verteilungstabelle zur \(\chi^2\)-Verteilung: Quantile nach ausgewählten Wahrscheinlichkeiten und Freiheitsgraden
|
|
p=
|
|
\(\nu\)
|
0.6
|
0.75
|
0.9
|
0.95
|
0.975
|
0.99
|
0.995
|
0.999
|
|
1
|
0.708
|
1.323
|
2.706
|
3.841
|
5.024
|
6.635
|
7.879
|
10.828
|
|
2
|
1.833
|
2.773
|
4.605
|
5.991
|
7.378
|
9.210
|
10.597
|
13.816
|
|
3
|
2.946
|
4.108
|
6.251
|
7.815
|
9.348
|
11.345
|
12.838
|
16.266
|
|
4
|
4.045
|
5.385
|
7.779
|
9.488
|
11.143
|
13.277
|
14.860
|
18.467
|
|
5
|
5.132
|
6.626
|
9.236
|
11.070
|
12.833
|
15.086
|
16.750
|
20.515
|
|
6
|
6.211
|
7.841
|
10.645
|
12.592
|
14.449
|
16.812
|
18.548
|
22.458
|
|
7
|
7.283
|
9.037
|
12.017
|
14.067
|
16.013
|
18.475
|
20.278
|
24.322
|
|
8
|
8.351
|
10.219
|
13.362
|
15.507
|
17.535
|
20.090
|
21.955
|
26.124
|
|
9
|
9.414
|
11.389
|
14.684
|
16.919
|
19.023
|
21.666
|
23.589
|
27.877
|
|
10
|
10.473
|
12.549
|
15.987
|
18.307
|
20.483
|
23.209
|
25.188
|
29.588
|
|
11
|
11.530
|
13.701
|
17.275
|
19.675
|
21.920
|
24.725
|
26.757
|
31.264
|
|
12
|
12.584
|
14.845
|
18.549
|
21.026
|
23.337
|
26.217
|
28.300
|
32.909
|
|
13
|
13.636
|
15.984
|
19.812
|
22.362
|
24.736
|
27.688
|
29.819
|
34.528
|
|
14
|
14.685
|
17.117
|
21.064
|
23.685
|
26.119
|
29.141
|
31.319
|
36.123
|
|
15
|
15.733
|
18.245
|
22.307
|
24.996
|
27.488
|
30.578
|
32.801
|
37.697
|
|
16
|
16.780
|
19.369
|
23.542
|
26.296
|
28.845
|
32.000
|
34.267
|
39.252
|
|
17
|
17.824
|
20.489
|
24.769
|
27.587
|
30.191
|
33.409
|
35.718
|
40.790
|
|
18
|
18.868
|
21.605
|
25.989
|
28.869
|
31.526
|
34.805
|
37.156
|
42.312
|
|
19
|
19.910
|
22.718
|
27.204
|
30.144
|
32.852
|
36.191
|
38.582
|
43.820
|
|
20
|
20.951
|
23.828
|
28.412
|
31.410
|
34.170
|
37.566
|
39.997
|
45.315
|
|
21
|
21.991
|
24.935
|
29.615
|
32.671
|
35.479
|
38.932
|
41.401
|
46.797
|
|
22
|
23.031
|
26.039
|
30.813
|
33.924
|
36.781
|
40.289
|
42.796
|
48.268
|
|
23
|
24.069
|
27.141
|
32.007
|
35.172
|
38.076
|
41.638
|
44.181
|
49.728
|
|
24
|
25.106
|
28.241
|
33.196
|
36.415
|
39.364
|
42.980
|
45.559
|
51.179
|
|
25
|
26.143
|
29.339
|
34.382
|
37.652
|
40.646
|
44.314
|
46.928
|
52.620
|
|
26
|
27.179
|
30.435
|
35.563
|
38.885
|
41.923
|
45.642
|
48.290
|
54.052
|
|
27
|
28.214
|
31.528
|
36.741
|
40.113
|
43.195
|
46.963
|
49.645
|
55.476
|
|
28
|
29.249
|
32.620
|
37.916
|
41.337
|
44.461
|
48.278
|
50.993
|
56.892
|
|
29
|
30.283
|
33.711
|
39.087
|
42.557
|
45.722
|
49.588
|
52.336
|
58.301
|
|
30
|
31.316
|
34.800
|
40.256
|
43.773
|
46.979
|
50.892
|
53.672
|
59.703
|
|
31
|
32.349
|
35.887
|
41.422
|
44.985
|
48.232
|
52.191
|
55.003
|
61.098
|
|
32
|
33.381
|
36.973
|
42.585
|
46.194
|
49.480
|
53.486
|
56.328
|
62.487
|
|
33
|
34.413
|
38.058
|
43.745
|
47.400
|
50.725
|
54.776
|
57.648
|
63.870
|
|
34
|
35.444
|
39.141
|
44.903
|
48.602
|
51.966
|
56.061
|
58.964
|
65.247
|
|
35
|
36.475
|
40.223
|
46.059
|
49.802
|
53.203
|
57.342
|
60.275
|
66.619
|
|
36
|
37.505
|
41.304
|
47.212
|
50.998
|
54.437
|
58.619
|
61.581
|
67.985
|
|
37
|
38.535
|
42.383
|
48.363
|
52.192
|
55.668
|
59.893
|
62.883
|
69.346
|
|
38
|
39.564
|
43.462
|
49.513
|
53.384
|
56.896
|
61.162
|
64.181
|
70.703
|
|
39
|
40.593
|
44.539
|
50.660
|
54.572
|
58.120
|
62.428
|
65.476
|
72.055
|
|
40
|
41.622
|
45.616
|
51.805
|
55.758
|
59.342
|
63.691
|
66.766
|
73.402
|
|
50
|
51.892
|
56.334
|
63.167
|
67.505
|
71.420
|
76.154
|
79.490
|
86.661
|
|
60
|
62.135
|
66.981
|
74.397
|
79.082
|
83.298
|
88.379
|
91.952
|
99.607
|
|
70
|
72.358
|
77.577
|
85.527
|
90.531
|
95.023
|
100.425
|
104.215
|
112.317
|
|
80
|
82.566
|
88.130
|
96.578
|
101.879
|
106.629
|
112.329
|
116.321
|
124.839
|
|
90
|
92.761
|
98.650
|
107.565
|
113.145
|
118.136
|
124.116
|
128.299
|
137.208
|
|
100
|
102.946
|
109.141
|
118.498
|
124.342
|
129.561
|
135.807
|
140.169
|
149.449
|