정규 분포

정규 분포는 연속 확률 분포입니다. 가우스 분포라고도합니다.

정규 분포 밀도 함수 f (z)는 종 모양을 닮았 기 때문에 종 곡선이라고합니다.

표준 정규 분포 테이블은 지정된 분포 범위의 확률을 찾기 위해 f ( z ) 함수 아래의 면적을 찾는 데 사용됩니다 .

정규 분포 함수

랜덤 변수 X에 정규 분포가있을 때

정규 분포의 확률 밀도 함수 및 누적 분포 함수 :

 

확률 밀도 함수 (pdf)

확률 밀도 함수는 다음과 같이 제공됩니다.

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

X는 랜덤 변수입니다.

μ는 평균값입니다.

σ는 표준 편차 (std) 값입니다.

e = 2.7182818 ... 상수.

π = 3.1415926 ... 상수.

 

누적 분포 함수

누적 분포 함수는 다음과 같이 제공됩니다.

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

X는 랜덤 변수입니다.

μ는 평균값입니다.

σ는 표준 편차 (std) 값입니다.

e = 2.7182818 ... 상수.

π = 3.1415926 ... 상수.

표준 정규 분포 함수

언제

그런 다음 표준 정규 분포의 확률 밀도 함수 및 누적 분포 함수 :

확률 밀도 함수

누적 분포 함수

표준 정규 분포표

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 2012 년 0 월
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

 

표준 정규 분포 그래프 (0 이상)

 

 

 

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