Phân phối chuẩn chỉnh là phân phối tỷ lệ liên tục. Nó còn gọi là phân phối Gaussian.

Bạn đang xem: Bảng tra phân phối chuẩn

Hàm mật độ phân phối chuẩn f (z) được call là Đường cong hình chuông vì chưng nó có hình dạng y như một dòng chuông.

Bảng phân phối chuẩn chỉnh chuẩn được thực hiện để tìm diện tích s dưới hàm f ( z ) nhằm mục tiêu tìm tỷ lệ của một phạm vi bày bán xác định.

Hàm trưng bày chuẩn

Khi biến ngẫu nhiên X bao gồm phân phối chuẩn,

*

*

*

Hàm mật độ xác suất và hàm triển lẵm tích lũy của bày bán chuẩn:

Hàm mật độ xác suất (pdf)

Hàm tỷ lệ xác suất được mang lại bởi:

*

X là đổi mới ngẫu nhiên.

μ là quý hiếm trung bình.

σ là quý hiếm độ lệch chuẩn (std).

e = 2,7182818 ... Hằng số.

Xem thêm: Kiến Thức Các Bài Toán Nâng Cao Lớp 7 Có Lời Giải ), 30 Đề Thi Học Sinh Giỏi Toán Lớp 7 Có Đáp Án

π = 3,1415926 ... Hằng số.

Chức năng cung cấp tích lũy

Hàm trưng bày tích lũy được cho bởi:

*

X là thay đổi ngẫu nhiên.

μ là giá trị trung bình.

σ là cực hiếm độ lệch chuẩn (std).

e = 2,7182818 ... Hằng số.

π = 3,1415926 ... Hằng số.

Hàm phân phối chuẩn chỉnh chuẩn

Khi nào

*

*

*

Khi đó, hàm mật độ xác suất và hàm bày bán tích lũy của phân phối chuẩn chỉnh chuẩn:

Hàm tỷ lệ xác suất

*

Chức năng triển lẵm tích lũy

*

Bảng phân phối chuẩn chỉnh chuẩn

z Φ ( z )φ ( z )
0,000,50000,3989
0,010,50400,3989
0,020,50800,3989
0,030,51200,3988
0,040,51600,3986
0,050,51990,3984
0,060,52390,3982
0,070,52790,3980
0,080,53190,3977
0,090,53590,3973
0,100,53980,3970
0,110,54380,3965
0,120,54780,3961
0,130,55170,3956
0,140,55570,3951
0,150,55960,3945
0,160,56360,3939
0,170,56750,3932
0,180,57140,3925
0,190,57530,3918
0,200,57930,3910
0,210,58320,3902
0,220,58710,3894
0,230,59100,3885
0,240,59480,3876
0,250,59870,3867
0,260,60260,3857
0,270,60640,3847
0,280,61030,3836
0,290,61410,3825
0,30 0,61790,3814
0,310,62170,3802
0,320,62550,3790
0,330,62930,3778
0,340,63310,3765
0,350,63680,3752
0,360,64060,3739
0,370,64430,3725
0,380,64800,3712
0,390,65170,3697
0,400,65540,3683
0,410,65910,3668
0,420,66280,3653
0,430,66640,3637
0,440,67000,3621
0,450,67360,3605
0,460,67720,3589
0,470,68080,3572
0,480,68440,3555
0,490,68790,3538
0,500,69150,3521
0,510,69500,3503
0,520,69850,3485
0,530,70190,3467
0,540,70540,3448
0,550,70880,3429
0,560,71230,3410
0,570,71570,3391
0,580,71900,3372
0,590,7224 0,3352
0,600,72570,3332
0,610,72910,3312
0,620,73240,3292
0,630,73570,3271
0,640,73890,3251
0,650,74220,3230
0,660,74540,3209
0,670,74860,3187
0,680,75170,3166
0,690,75490,3144
0,700,75800,3123
0,710,76110,3101
0,720,76420,3079
0,730,76730,3056
0,740,77040,3034
0,750,77340,3011
0,760,77640,2989
0,770,77940,2966
0,780,78230,2943
0,790,78520,2920
0,800,78810,2897
0,810,79100,2874
0,820,79390,2850
0,830,79670,2827
0,840,79950,2803
0,850,80230,2780
0,860,80510,2756
0,870,80780,2732
0,880,81060,2709
0,890,81330,2685
0,900,81590,2661
0,910,81860,2637
0,920,82120,2613
0,930,82380,2589
0,940,82640,2565
0,950,82890,2541
0,960,83150,2516
0,970,83400,2492
0,980,83650,2468
0,990,83890,2444
1,000,84130,2420
1,010,84380,2396
1,020,84610,2371
1,030,84850,2347
1,040,85080,2323
1,050,85310,2299
1,060,85540,2275
1,070,85770,2251
1,080,85990,2227
1,090,86210,2203
1.100,86430,2179
1.110,86650,2155
1.120,86860,2131
1.130,87080,2107
1,140,87290,2083
1,150,87490,2059
1.160,87700,2036
1.170,87900,2012
1.180,88100,1989
1.190,88300,1965
1,200,88490,1942
1,210,88690,1919
1,220,88880,1895
1,230,89070,1872
1,240,89250,1849
1,250,89440,1826
1,260,89620,1804
1,270,89800,1781
1,280,89970,1758
1,290,90150,1736
1,300,90320,1714
1,310,90490,1691
1,320,90660,1669
1,330,90820,1647
1,340,90990,1626
1,350,91150,1604
1,360,91310,1582
1,370,91470,1561
1,380,91620,1539
1,390,91770,1518
1,400,91920,1497
1,410,92070,1476
1,420,92220,1456
1,430,92360,1435
1,440,92510,1415
1,450,92650,1394
1,460,92790,1374
1,47 0,92920,1354
1,480,93060,1334
1,490,93190,1315
1,500,93320,1295
1.510,93450,1276
1,520,93570,1257
1.530,93700,1238
1.540,93820,1219
1.550,93940,1200
1.560,94060,1182
1.570,94180,1163
1.580,94290,1145
1.590,94410,1127
1,600,94520,1109
1,610,94630,1092
1,620,94740,1074
1,630,94840,1057
1,640,94950,1040
1,650,95050,1023
1,660,95150,1006
1,670,95250,0989
1,680,95350,0973
1,690,95450,0957
1,700,95540,0940
1,710,95640,0925
1,720,95730,0909
1,730,95820,0893
1,740,95910,0878
1,750,95990,0863
1,760,9608 0,0848
1,770,96160,0833
1,780,96250,0818
1,790,96330,0804
1,800,96410,0790
1,810,96490,0775
1,820,96560,0761
1.830,96640,0748
1,840,96710,0734
1,850,96780,0721
1,860,96860,0707
1.870,96930,0694
1,880,96990,0681
1,890,97060,0669
1,900,97130,0656
1,910,97190,0644
1,920,97260,0632
1,930,97320,0620
1,940,97380,0608
1,950,97440,0596
1,960,97500,0584
1,970,97560,0573
1,980,97610,0562
1,990,97670,0551
2,000,97720,0540
2,010,97780,0529
2.020,97830,0519
2,030,97880,0508
2,040,97930,0498
2,050,97980,0488
2,060,98030,0478
2,070,98080,0468
2,080,98120,0459
2,090,98170,0449
2,100,98210,0440
2,110,98260,0431
2,120,98300,0422
2,130,98340,0413
2,140,98380,0404
2,150,98420,0396
2,160,98460,0387
2,170,98500,0379
2,180,98540,0371
2,190,98570,0363
2,200,98610,0355
2,210,98640,0347
2,220,98680,0339
2,230,98710,0332
2,240,98750,0325
2,250,98780,0317
2,260,98810,0310
2,270,98840,0303
2,280,98870,0297
2,290,98900,0290
2,300,98930,0283
2,310,98960,0277
2,320,98980,0270
2,330,99010,0264
2,340,99040,0258
2,350,99060,0252
2,360,99090,0246
2,370,99110,0241
2,380,99130,0235
2,390,99160,0229
2,400,99180,0224
2,410,99200,0219
2,420,99220,0213
2,430,99250,0208
2,440,99270,0203
2,450,99290,0198
2,460,99310,0194
2,470,99320,0189
2,480,99340,0184
2,490,99360,0180
2,500,99380,0175
2,510,99400,0171
2,520,99410,0167
2,530,99430,0163
2,540,99450,0158
2,550,99460,0154
2,560,99480,0151
2,570,99490,0147
2,580,99510,0143
2,590,99520,0139
2,600,99530,0136
2,610,99550,0132
2,620,99560,0129
2,630,99570,0126
2,640,99590,0122
2,650,99600,0119
2,660,99610,0116
2,670,99620,0113
2,680,99630,0110
2,690,99640,0107
2,700,99650,0104
2,710,99660,0101
2,720,99670,0099
2,730,99680,0096
2,740,99690,0093
2,750,99700,0091
2,760,99710,0088
2,770,99720,0086
2,780,99730,0084
2,790,99740,0081
2,800,99740,0079
2,810,99750,0077
2,820,99760,0075
2,830,99770,0073
2,840,99770,0071
2,850,99780,0069
2,860,99790,0067
2,870,99790,0065
2,880,99800,0063
2,890,99810,0061
2,900,99810,0060
2,910,99820,0058
2,920,99820,0056
2,930,99830,0055
2,940,99840,0053
2,950,99840,0051
2,960,99850,0050
2,970,99850,0048
2,980,99860,0047
2,990,99860,0046
3,000,99870,0044
3.010,99870,0043
3.020,99870,0042
3.030,99880,0040
3.040,99880,0039
3.050,99890,0038
3.060,99890,0037
3.070,99890,0036
3.080,99900,0035
3.090,99900,0034
3,100,99900,0033
3,110,99910,0032
3,120,99910,0031
3,130,99910,0030
3,140,99920,0029
3,150,99920,0028
3,160,99920,0027
3,170,99920,0026
3,180,99930,0025
3,190,99930,0025
3,200,99930,0024
3,210,99930,0023
3,220,99940,0022
3,230,99940,0022
3,240,99940,0021
3,250,99940,0020
3,260,99940,0020
3,270,99950,0019
3,280,99950,0018
3,290,99950,0018
3,300,99950,0017
3,310,99950,0017
3,320,99950,0016
3,330,99960,0016
3,340,99960,0015
3,350,99960,0015
3,360,99960,0014
3,370,99960,0014
3,380,99960,0013
3,390,99970,0013
3,400,99970,0012
3,410,99970,0012
3,420,99970,0012
3,430,99970,0011
3,440,99970,0011
3,450,99970,0010
3,460,99970,0010
3,470,99980,0010
3,480,99980,0009
3,490,99980,0009
3,500,99980,0009
3.510,99980,0008
3.520,99980,0008
3.530,99980,0008
3.540,99980,0008
3.550,99980,0007
3,560,99980,0007
3.570,99980,0007
3.580,99980,0007
3,590,99980,0006
3,600,99980,0006
3,610,99980,0006
3,620,99990,0006
3,630,99990,0005
3,640,99990,0005
3,650,99990,0005
3,660,99990,0005
3,670,99990,0005
3,680,99990,0005
3,690,99990,0004
3,700,99990,0004
3,710,99990,0004
3,720,99990,0004
3,730,99990,0004
3,740,99990,0004
3,750,99990,0004
3,760,99990,0003
3,770,99990,0003
3,780,99990,0003
3,790,99990,0003
3,800,99990,0003
3,810,99990,0003
3,820,99990,0003
3,830,99990,0003
3,840,99990,0003
3,850,99990,0002
3,860,99990,0002
3,870,99990,0002
3,880,99990,0002
3,890,99990,0002
3,901,00000,0002
3,911,00000,0002
3,921,00000,0002
3,931,00000,0002
3,941,00000,0002
3,951,00000,0002
3,961,00000,0002
3,971,00000,0002
3,981,00000,0001
3,991,00000,0001