Normal dağılım

Normal dağılım, sürekli bir olasılık dağılımıdır. Gauss dağılımı olarak da adlandırılır.

Normal dağılım yoğunluğu fonksiyonu f (z), bir zile benzeyen bir şekle sahip olduğu için Çan Eğrisi olarak adlandırılır.

Standart normal dağılım tablosu, belirli bir dağılım aralığının olasılığını bulmak için f ( z ) fonksiyonunun altındaki alanı bulmak için kullanılır .

Normal dağılım işlevi

Rastgele değişken X normal dağılıma sahip olduğunda,

Normal dağılımın olasılık yoğunluk fonksiyonu ve kümülatif dağılım fonksiyonu:

 

Olasılık yoğunluk işlevi (pdf)

Olasılık yoğunluk fonksiyonu şu şekilde verilir:

f_ {X} (x) = \ frac {1} {\ sigma \ sqrt {2 \ pi}} e ^ {- \ frac {(x- \ mu) ^ 2} {2 \ sigma ^ 2}}

X rastgele değişkendir.

μ ortalama değerdir.

σ, standart sapma (std) değeridir.

e = 2,7182818 ... sabit.

π = 3.1415926 ... sabit.

 

Kümülatif dağılım fonksiyonu

Kümülatif dağılım işlevi şu şekilde verilir:

F_ {X} (x) = \ frac {1} {\ sigma \ sqrt {2 \ pi}} \ int _ {- \ infty} ^ {x} e ^ {- \ frac {(y- \ mu) ^ 2 } {2 \ sigma ^ 2}} dy

X rastgele değişkendir.

μ ortalama değerdir.

σ, standart sapma (std) değeridir.

e = 2,7182818 ... sabit.

π = 3.1415926 ... sabit.

Standart normal dağılım işlevi

Ne zaman

Daha sonra olasılık yoğunluk fonksiyonu ve standart normal dağılımın kümülatif dağılım fonksiyonu:

Olasılık yoğunluk işlevi

Kümülatif dağılım fonksiyonu

Standart normal dağılım tablosu

z Φ ( z ) φ ( z )
0.00 0.5000 0,3989
0.01 0,5040 0,3989
0.02 0,5080 0,3989
0.03 0.5120 0,3988
0.04 0.5160 0,3986
0.05 0.5199 0.3984
0.06 0.5239 0.3982
0.07 0.5279 0,3980
0.08 0.5319 0,3977
0.09 0.5359 0,3973
0.10 0,5398 0,3970
0.11 0.5438 0,3965
0.12 0.5478 0,3961
0.13 0,5517 0,3956
0.14 0,5557 0,3951
0.15 0.5596 0,3945
0.16 0,5636 0,3939
0.17 0.5675 0,3932
0.18 0.5714 0,3925
0.19 0.5753 0,3918
0.20 0.5793 0,3910
0.21 0,5832 0,3902
0.22 0,5871 0,3894
0.23 0.5910 0.3885
0.24 0,5948 0,3876
0.25 0.5987 0,3867
0.26 0.6026 0,3857
0.27 0.6064 0,3847
0.28 0.6103 0,3836
0.29 0.6141 0,3825
0.30 0.6179 0,3814
0.31 0.6217 0.3802
0.32 0.6255 0,3790
0.33 0.6293 0,3778
0.34 0.6331 0,3765
0.35 0.6368 0.3752
0.36 0.6406 0,3739
0.37 0.6443 0,3725
0.38 0.6480 0,3712
0.39 0.6517 0.3697
0.40 0.6554 0.3683
0.41 0.6591 0,3668
0.42 0.6628 0.3653
0.43 0.6664 0,3637
0.44 0.6700 0,3621
0.45 0.6736 0.3605
0.46 0.6772 0,3589
0.47 0.6808 0,3572
0.48 0.6844 0.3555
0.49 0.6879 0,3538
0.50 0.6915 0,3521
0.51 0,6950 0,3503
0.52 0.6985 0.3485
0.53 0.7019 0,3467
0.54 0.7054 0,3448
0.55 0.7088 0,3429
0.56 0.7123 0,3410
0.57 0.7157 0.3391
0.58 0.7190 0,3372
0.59 0.7224 0.3352
0.60 0.7257 0,3332
0.61 0.7291 0,3312
0.62 0.7324 0,3292
0.63 0.7357 0.3271
0.64 0.7389 0.3251
0.65 0.7422 0,3230
0.66 0.7454 0.3209
0.67 0.7486 0,3187
0.68 0.7517 0.3166
0.69 0.7549 0,3144
0.70 0.7580 0.3123
0.71 0.7611 0.3101
0.72 0.7642 0.3079
0.73 0.7673 0.3056
0.74 0.7704 0.3034
0.75 0.7734 0.3011
0.76 0.7764 0,2989
0.77 0.7794 0.2966
0.78 0.7823 0.2943
0.79 0.7852 0.2920
0.80 0.7881 0.2897
0.81 0.7910 0,2874
0.82 0,7939 0.2850
0.83 0,7967 0,2827
0.84 0.7995 0.2803
0.85 0.8023 0.2780
0.86 0.8051 0.2756
0.87 0.8078 0.2732
0.88 0.8106 0.2709
0.89 0.8133 0.2685
0.90 0.8159 0.2661
0.91 0.8186 0.2637
0.92 0.8212 0.2613
0.93 0.8238 0.2589
0.94 0.8264 0.2565
0.95 0.8289 0.2541
0.96 0.8315 0.2516
0.97 0.8340 0.2492
0.98 0.8365 0.2468
0,99 0.8389 0.2444
1.00 0.8413 0.2420
1.01 0.8438 0.2396
1.02 0.8461 0.2371
1.03 0.8485 0.2347
1.04 0.8508 0.2323
1.05 0.8531 0.2299
1.06 0.8554 0.2275
1.07 0.8577 0.2251
1.08 0.8599 0.2227
1.09 0.8621 0.2203
1.10 0.8643 0.2179
1.11 0.8665 0.2155
1.12 0.8686 0.2131
1.13 0.8708 0.2107
1.14 0.8729 0.2083
1.15 0.8749 0.2059
1.16 0.8770 0.2036
1.17 0.8790 0.2012
1.18 0.8810 0,1989
1.19 0.8830 0,1965
1.20 0.8849 0.1942
1.21 0.8869 0.1919
1.22 0.8888 0,1895
1.23 0.8907 0.1872
1.24 0.8925 0.1849
1.25 0.8944 0.1826
1.26 0.8962 0.1804
1.27 0.8980 0.1781
1.28 0.8997 0.1758
1.29 0.9015 0.1736
1.30 0.9032 0.1714
1.31 0.9049 0.1691
1.32 0.9066 0.1669
1.33 0.9082 0.1647
1.34 0.9099 0.1626
1.35 0.9115 0.1604
1.36 0.9131 0.1582
1.37 0.9147 0.1561
1.38 0.9162 0.1539
1.39 0.9177 0.1518
1.40 0.9192 0.1497
1.41 0.9207 0.1476
1.42 0.9222 0.1456
1.43 0.9236 0,1435
1.44 0.9251 0.1415
1.45 0.9265 0.1394
1.46 0.9279 0.1374
1.47 0.9292 0.1354
1.48 0.9306 0.1334
1.49 0.9319 0.1315
1.50 0.9332 0.1295
1.51 0.9345 0.1276
1.52 0.9357 0.1257
1.53 0.9370 0.1238
1.54 0.9382 0.1219
1.55 0.9394 0.1200
1.56 0.9406 0.1182
1.57 0.9418 0.1163
1.58 0.9429 0.1145
1.59 0.9441 0.1127
1.60 0.9452 0.1109
1.61 0.9463 0.1092
1.62 0.9474 0.1074
1.63 0.9484 0.1057
1.64 0.9495 0.1040
1.65 0.9505 0.1023
1.66 0.9515 0.1006
1.67 0.9525 0,0989
1.68 0.9535 0,0973
1.69 0.9545 0,0957
1.70 0.9554 0,0940
1.71 0.9564 0,0925
1.72 0.9573 0.0909
1.73 0.9582 0,0893
1.74 0.9591 0,0878
1.75 0.9599 0.0863
1.76 0.9608 0,0848
1.77 0.9616 0,0833
1.78 0.9625 0,0818
1.79 0.9633 0.0804
1.80 0.9641 0,0790
1.81 0.9649 0,0775
1.82 0.9656 0,0761
1.83 0.9664 0,0748
1.84 0.9671 0,0734
1.85 0.9678 0,0721
1.86 0.9686 0.0707
1.87 0.9693 0,0694
1.88 0,9699 0.0681
1.89 0.9706 0.0669
1.90 0.9713 0,0656
1.91 0.9719 0,0644
1.92 0.9726 0,0632
1.93 0.9732 0,0620
1.94 0.9738 0.0608
1.95 0.9744 0.0596
1.96 0.9750 0.0584
1.97 0.9756 0.0573
1.98 0.9761 0,0562
1.99 0.9767 0,0551
2.00 0.9772 0.0540
2.01 0.9778 0.0529
2.02 0.9783 0.0519
2.03 0.9788 0,0508
2.04 0.9793 0.0498
2.05 0.9798 0.0488
2.06 0.9803 0.0478
2.07 0.9808 0,0468
2.08 0.9812 0,0459
2.09 0.9817 0.0449
2.10 0.9821 0,0440
2.11 0.9826 0,0431
2.12 0.9830 0,0422
2.13 0.9834 0,0413
2.14 0.9838 0,0404
2.15 0.9842 0,0396
2.16 0.9846 0.0387
2.17 0.9850 0,0379
2.18 0.9854 0,0371
2.19 0.9857 0,0363
2.20 0.9861 0,0355
2.21 0.9864 0,0347
2.22 0.9868 0,0339
2.23 0.9871 0,0332
2.24 0.9875 0,0325
2.25 0.9878 0,0317
2.26 0.9881 0,0310
2.27 0.9884 0,0303
2.28 0.9887 0,0297
2.29 0.9890 0,0290
2.30 0.9893 0,0283
2.31 0.9896 0,0277
2.32 0.9898 0,0270
2.33 0.9901 0,0264
2.34 0.9904 0,0258
2.35 0.9906 0,0252
2.36 0.9909 0,0246
2.37 0.9911 0.0241
2.38 0.9913 0,0235
2.39 0.9916 0,0229
2.40 0.9918 0,0224
2.41 0.9920 0,0219
2.42 0.9922 0,0213
2.43 0.9925 0,0208
2.44 0.9927 0,0203
2.45 0.9929 0.0198
2.46 0.9931 0.0194
2.47 0.9932 0,0189
2.48 0.9934 0,0184
2.49 0.9936 0.0180
2.50 0.9938 0,0175
2.51 0.9940 0,0171
2.52 0.9941 0.0167
2.53 0.9943 0,0163
2.54 0.9945 0,0158
2.55 0.9946 0,0154
2.56 0.9948 0,0151
2.57 0.9949 0,0147
2.58 0.9951 0,0143
2.59 0.9952 0,0139
2.60 0.9953 0.0136
2.61 0.9955 0.0132
2.62 0.9956 0,0129
2.63 0.9957 0,0126
2.64 0.9959 0,0122
2.65 0.9960 0.0119
2.66 0.9961 0.0116
2.67 0.9962 0,0113
2.68 0.9963 0.0110
2.69 0.9964 0.0107
2.70 0.9965 0,0104
2.71 0.9966 0,0101
2.72 0.9967 0.0099
2.73 0.9968 0.0096
2.74 0.9969 0.0093
2.75 0.9970 0.0091
2.76 0.9971 0.0088
2.77 0.9972 0.0086
2.78 0.9973 0.0084
2.79 0.9974 0.0081
2.80 0.9974 0.0079
2.81 0.9975 0.0077
2.82 0.9976 0.0075
2.83 0.9977 0.0073
2.84 0.9977 0.0071
2.85 0.9978 0.0069
2.86 0.9979 0.0067
2.87 0.9979 0.0065
2.88 0.9980 0.0063
2.89 0.9981 0.0061
2.90 0.9981 0.0060
2.91 0.9982 0.0058
2.92 0.9982 0.0056
2.93 0.9983 0.0055
2.94 0.9984 0.0053
2.95 0.9984 0.0051
2.96 0.9985 0.0050
2.97 0.9985 0.0048
2.98 0.9986 0.0047
2.99 0.9986 0.0046
3.00 0.9987 0.0044
3.01 0.9987 0.0043
3.02 0.9987 0.0042
3.03 0.9988 0.0040
3.04 0.9988 0.0039
3.05 0.9989 0.0038
3.06 0.9989 0.0037
3.07 0.9989 0.0036
3.08 0.9990 0.0035
3.09 0.9990 0.0034
3.10 0.9990 0.0033
3.11 0.9991 0.0032
3.12 0.9991 0.0031
3.13 0.9991 0.0030
3.14 0.9992 0.0029
3.15 0.9992 0.0028
3.16 0.9992 0.0027
3.17 0.9992 0.0026
3.18 0.9993 0.0025
3.19 0.9993 0.0025
3.20 0.9993 0.0024
3.21 0.9993 0.0023
3.22 0.9994 0.0022
3.23 0.9994 0.0022
3.24 0.9994 0.0021
3.25 0.9994 0.0020
3.26 0.9994 0.0020
3.27 0.9995 0.0019
3.28 0.9995 0.0018
3.29 0.9995 0.0018
3.30 0.9995 0.0017
3.31 0.9995 0.0017
3.32 0.9995 0.0016
3.33 0.9996 0.0016
3.34 0.9996 0.0015
3.35 0.9996 0.0015
3.36 0.9996 0.0014
3.37 0.9996 0.0014
3.38 0.9996 0.0013
3.39 0.9997 0.0013
3.40 0.9997 0.0012
3.41 0.9997 0.0012
3.42 0.9997 0.0012
3.43 0.9997 0.0011
3.44 0.9997 0.0011
3.45 0.9997 0.0010
3.46 0.9997 0.0010
3.47 0.9998 0.0010
3.48 0.9998 0.0009
3.49 0.9998 0.0009
3.50 0.9998 0.0009
3.51 0.9998 0.0008
3.52 0.9998 0.0008
3.53 0.9998 0.0008
3.54 0.9998 0.0008
3.55 0.9998 0.0007
3.56 0.9998 0.0007
3.57 0.9998 0.0007
3.58 0.9998 0.0007
3.59 0.9998 0.0006
3.60 0.9998 0.0006
3.61 0.9998 0.0006
3.62 0.9999 0.0006
3.63 0.9999 0.0005
3.64 0.9999 0.0005
3.65 0.9999 0.0005
3.66 0.9999 0.0005
3.67 0.9999 0.0005
3.68 0.9999 0.0005
3.69 0.9999 0.0004
3.70 0.9999 0.0004
3.71 0.9999 0.0004
3.72 0.9999 0.0004
3.73 0.9999 0.0004
3.74 0.9999 0.0004
3.75 0.9999 0.0004
3.76 0.9999 0.0003
3.77 0.9999 0.0003
3.78 0.9999 0.0003
3.79 0.9999 0.0003
3.80 0.9999 0.0003
3.81 0.9999 0.0003
3.82 0.9999 0.0003
3.83 0.9999 0.0003
3.84 0.9999 0.0003
3.85 0.9999 0.0002
3.86 0.9999 0.0002
3.87 0.9999 0.0002
3.88 0.9999 0.0002
3.89 0.9999 0.0002
3.90 1.0000 0.0002
3.91 1.0000 0.0002
3.92 1.0000 0.0002
3.93 1.0000 0.0002
3.94 1.0000 0.0002
3.95 1.0000 0.0002
3.96 1.0000 0.0002
3.97 1.0000 0.0002
3.98 1.0000 0.0001
3.99 1.0000 0.0001

 

Standart Normal Dağılım Grafiği (sıfırın üstünde)

 

 

 

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