标准正态分布函数数值表75286

整理文本标准正态分布函数数值表

φ( x ) =

φ( - x ) = 1 –φ( x )

φ(x) x

x 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

2.9 0.5000

0.5398

0.5793

0.6179

0.6554

0.6915

0.7257

0.7580

0.7881

0.8159

0.8413

0.8643

0.8849

0.9032

0.9192

0.9332

0.9452

0.9554

0.9641

0.9713

0.9772

0.9821

0.9861

0.9893

0.9918

0.9938

0.9953

0.9965

0.9974

0.9981 0.5040

0.5438

0.5832

0.6217

0.6591

0.6950

0.7291

0.7611

0.7910

0.8186

0.8438

0.8665

0.8869

0.9049

0.9207

0.9345

0.9463

0.9564

0.9648

0.9719

0.9778

0.9826

0.9864

0.9896

0.9920

0.9940

0.9955

0.9966

0.9975

0.9982 0.5080

0.5478

0.5871

0.6255

0.6628

0.6985

0.7324

0.7642

0.7939

0.8212

0.8461

0.8686

0.8888

0.9066

0.9222

0.9357

0.9474

0.9573

0.9656

0.9726

0.9783

0.9830

0.9868

0.9898

0.9922

0.9941

0.9956

0.9967

0.9976

0.9982 0.5120

0.5517

0.5910

0.6293

0.6664

0.7019

0.7357

0.7673

0.7967

0.8238

0.8485

0.8708

0.8907

0.9082

0.9236

0.9370

0.9484

0.9582

0.9664

0.9732

0.9788

0.9834

0.9871

0.9901

0.9925

0.9943

0.9957

0.9968

0.9977

0.9983 0.5160

0.5557

0.5948

0.6331

0.6700

0.7054

0.7389

0.7703

0.7995

0.8264

0.8508

0.8729

0.8925

0.9099

0.9251

0.9382

0.9495

0.9591

0.9671

0.9738

0.9793

0.9838

0.9874

0.9904

0.9927

0.9945

0.9959

0.9969

0.9977

0.9984 0.5199

0.5596

0.5987

0.6368

0.6736

0.7088

0.7422

0.7734

0.8023

0.8289

0.8531

0.8749

0.8944

0.9115

0.9265

0.9394

0.9505

0.9599

0.9678

0.9744

0.9798

0.9842

0.9878

0.9906

0.9929

0.9946

0.9960

0.9970

0.9978

0.9984 0.5239

0.5636

0.6026

0.6406

0.6772

0.7123

0.7454

0.7764

0.8051

0.8315

0.8554

0.8770

0.8962

0.9131

0.9278

0.9406

0.9515

0.9608

0.9686

0.9750

0.9803

0.9846

0.9881

0.9909

0.9931

0.9948

0.9961

0.9971

0.9979

0.9985 0.5279

0.5675

0.6064

0.6443

0.6808

0.7157

0.7486

0.7794

0.8078

0.8340

0.8577

0.8790

0.8980

0.9147

0.9292

0.9418

0.9525

0.9616

0.9693

0.9756

0.9808

0.9850

0.9884

0.9911

0.9932

0.9949

0.9962

0.9972

0.9979

0.9985 0.5319

0.5714

0.6103

0.6480

0.6844

0.7190

0.7517

0.7823

0.8106

0.8365

0.8599

0.8810

0.8997

0.9162

0.9306

0.9430

0.9535

0.9625

0.9700

0.9762

0.9812

0.9854

0.9887

0.9913

0.9934

0.9951

0.9963

0.9973

0.9980

0.9986 0.5359

0.5753

0.6141

0.6517

0.6879

0.7224

0.7549

0.7852

0.8133

0.8389

0.8621

0.8830

0.9015

0.9177

0.9319

0.9441

0.9545

0.9633

0.9706

0.9767

0.9817

0.9857

0.9890

0.9916

0.9936

0.9952

0.9964

0.9974

0.9981

0.9986

3.0 0.9987 0.9990 0.9993 0.9995 0.9997 0.9998 0.9998 0.9999 0.9999 1.0000

注：本表最后一行自左至右依次是φ(3.0)、…、φ(3.9)的值

合集下载

标准正态分布表

φ(x) x x00.50.5040.5080.512

0.5160.51990.52390.52790.53190.53590.1

0.5398

0.54380.54780.55170.55570.55960.56360.56750.57140.57530.20.57930.58320.58710.5910.59480.59870.60260.60640.61030.61410.30.61790.62170.62550.62930.63310.63680.64060.64430.6480.65170.40.65540.65910.66280.66640.670.67360.67720.68080.68440.68790.50.69150.6950.69850.70190.70540.70880.71230.71570.7190.72240.60.72570.72910.73240.73570.73890.74220.74540.74860.75170.75490.70.7580.76110.76420.76730.77030.77340.77640.77940.78230.78520.80.78810.7910.79390.79670.79950.80230.80510.80780.81060.81330.90.81590.81860.82120.82380.82640.82890.83150.8340.83650.838910.84130.84380.84610.84850.85080.85310.85540.85770.85990.86211.10.86430.86650.86860.87080.87290.87490.8770.8790.8810.8831.20.88490.88690.88880.89070.89250.89440.89620.8980.89970.90151.30.90320.90490.90660.90820.90990.91150.91310.91470.91620.91771.40.91920.92070.92220.92360.92510.92650.92780.92920.93060.93191.50.93320.93450.93570.9370.93820.93940.94060.94180.9430.94411.60.94520.94630.94740.94840.94950.95050.95150.95250.95350.95451.70.95540.95640.95730.95820.95910.95990.96080.96160.96250.96331.80.96410.96480.96560.96640.96710.96780.96860.96930.970.97061.90.97130.97190.97260.97320.97380.97440.9750.97560.97620.976720.97720.97780.97830.97880.97930.97980.98030.98080.98120.98172.10.98210.98260.9830.98340.98380.98420.98460.9850.98540.98572.20.98610.98640.98680.98710.98740.98780.98810.98840.98870.9892.30.98930.98960.98980.99010.99040.99060.99090.99110.99130.99162.40.99180.9920.99220.99250.99270.99290.99310.99320.99340.99362.50.99380.9940.99410.99430.99450.99460.99480.99490.99510.99522.60.99530.99550.99560.99570.99590.9960.99610.99620.99630.99642.70.99650.99660.99670.99680.99690.9970.99710.99720.99730.99742.80.99740.99750.99760.99770.99770.99780.99790.99790.9980.99812.90.99810.99820.99820.99830.99840.99840.99850.99850.99860.998630.99870.9990.99930.99950.99970.99980.99980.99990.999913.10.9990320.9990650.9990960.9991260.9991550.9991840.9992110.9992380.9992640.9992893.20.9993130.9993360.9993590.9993810.9994020.9994230.9994430.9994620.9994810.9994993.30.9995170.9995340.9995500.9995660.9995810.9995960.9996100.9996240.9996380.9996603.40.9996630.9996750.9996870.9996980.9997090.9997200.9997300.9997400.9997490.9997603.50.9997670.9997760.9997840.9997920.9998000.9998070.9998150.9998220.9998280.9998853.60.9998410.9998470.9998530.9998580.9998640.9998690.9998740.9998790.9998830.9998803.70.9998920.9998960.9999000.9999040.9999080.9999120.9999150.9999180.9999220.9999263.80.9999280.9999310.9999330.9999360.9999380.9999410.9999430.9999460.9999480.9999503.90.9999520.9999540.9999560.9999580.9999590.9999610.9999630.9999640.9999660.99996740.9999680.9999700.9999710.9999720.9999730.9999740.9999750.9999760.9999770.9999784.10.9999790.9999800.9999810.9999820.9999830.9999830.9999840.9999850.9999850.9999864.20.9999870.9999870.9999880.9999880.9999890.9999890.9999900.9999900.9999910.9999914.30.9999910.9999920.9999920.9999300.9999930.9999930.9999930.9999940.9999940.9999944.40.9999950.9999950.9999950.9999950.9999960.9999960.9999961.0000000.9999960.9999964.50.9999970.9999970.9999970.9999970.9999970.9999970.9999970.9999980.9999980.9999984.60.9999980.9999980.9999980.9999980.9999980.9999980.9999980.9999980.9999990.9999994.70.9999990.9999990.9999990.9999990.9999990.9999990.9999990.9999990.9999990.9999994.80.9999990.9999990.9999990.9999990.9999990.9999990.9999990.9999990.9999990.9999994.91.0000001.0000001.0000001.0000001.0000001.0000001.0000001.0000001.0000001.0000000.040.050.060.07标准正态分布函数表（形式1）

标准正态分布数值表

标准正态分布是统计学中非常重要的一种概率分布，它的数值表对于统计分析和研究具有重要的参考价值。标准正态分布数值表是一种以标准正态分布为基础的统计表格，通过这个表格可以方便地查找标准正态分布的各种概率值和临界值。本文将介绍标准正态分布数值表的基本结构和使用方法，希望能帮助读者更好地理解和运用标准正态分布数值表。

标准正态分布数值表通常包括两部分内容，一部分是标准正态分布的累积分布函数值，另一部分是标准正态分布的临界值。累积分布函数值是指标准正态分布随机变量小于或等于某一给定值的概率，而临界值则是指给定概率下对应的标准正态分布随机变量取值。在实际应用中，我们常常需要根据已知的概率值来查找对应的临界值，或者根据已知的临界值来查找对应的概率值，这时就需要用到标准正态分布数值表。

标准正态分布数值表的使用方法相对简单，首先需要确定所需查找的数值类型（累积分布函数值或临界值），然后根据给定的概率或取值范围，在数值表中查找对应的数值。在查找过程中，需要注意数值表中的行和列分别对应着标准正态分布的小数部分和百分数部分，因此需要将给定的概率值或取值范围转化为标准正态分布的百分数形式，再在数值表中进行查找。最后根据查找到的数值，即可得到对应的标准正态分布数值。

在实际应用中，标准正态分布数值表可以帮助我们进行各种统计推断和假设检验。例如，在进行样本均值的假设检验时，我们常常需要根据显著性水平来确定临界值，而这些临界值就可以通过标准正态分布数值表来查找得到。此外，标准正态分布数值表还可以帮助我们计算正态分布的概率值，从而进行概率推断和预测。

总之，标准正态分布数值表是统计学中一项非常重要的工具，它为我们提供了便利的数值查找方法，帮助我们更好地理解和运用标准正态分布。通过学习和掌握标准正态分布数值表的使用方法，我们可以更加灵活地进行统计分析和研究，为科学决策和实践应用提供有力的支持。希望本文能够帮助读者更好地理解标准正态分布数值表，并在实际应用中发挥其重要作用。

标准正态分布表 2

φ( - x ) = 1 –φ( x )

x0.0

0.010.020.030.040.050.060.070.080.09

0.00.500 00.504 00.508 00.512 00.516 00.519 90.523 90.527 90.531 90.535 9

0.10.539 80.543 80.547 80.551 70.555 70.559 60.563 60.567 50.571 40.575 3

0.20.579 30.583 20.587 10.591 00.594 80.598 70.602 60.606 40.610 30.614 1

0.30.617 90.621 70.625 50.629 30.633 10.636 80.640 40.644 30.648 00.651 7

0.40.655 40.659 10.662 80.666 40.670 00.673 60.677 20.680 80.684 40.687 9

0.50.691 50.695 00.698 50.701 90.705 40.708 80.712 30.715 70.719 00.722 4

0.60.725 70.729 10.732 40.735 70.738 90.742 20.745 40.748 60.751 70.754 9

0.70.758 00.761 10.764 20.767 30.770 30.773 40.776 40.779 40.782 30.785 2

0.80.788 10.791 00.793 90.796 70.799 50.802 30.805 10.807 80.810 60.813 3

0.90.815 90.818 60.821 20.823 80.826 40.828 90.835 50.834 00.836 50.838 9

10.841 30.843 80.846 10.848 50.850 80.853 10.855 40.857 70.859 90.862 1

标准正态分布-Z值表

0.000.010.020.030.040.050.060.070.080.09

0.00.500000.496010.492020.488030.484050.480060.476080.472100.468120.46414

0.10.460170.456200.452240.448280.444330.440380.436440.432510.428580.42465

0.20.420740.416830.412940.409050.405170.401290.397430.393580.389740.38591

0.30.382090.378280.374480.370700.366930.363170.359420.355690.351970.34827

0.40.344580.340900.337240.333600.329970.326360.322760.319180.315610.31207

0.50.308540.305030.301530.298060.294600.291160.287740.284340.280960.27760

0.60.274250.270930.267630.264350.261090.257850.254630.251430.248250.24510

0.70.241960.238850.235760.232700.229650.226630.223630.220650.217700.21476

0.80.211860.208970.206110.203270.200450.197660.194890.192150.189430.18673

0.90.184060.181410.178790.176190.173610.171060.168530.166020.163540.16109

1.00.158660.156250.153860.151510.149170.146860.144570.142310.140070.13786

标准正态分布函数数值表

鸟欲高飞先振翅，人求上进先读书。——李苦禅

标准正态分布函数数值表

φ(x)=

φ(-x)=1-φ(x)

φ(x)x

x0.000.010.020.030.040.050.060.070.080.090.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5 1.6

1.7

1.8

1.9

2.0

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

2.90.5000

0.5398

0.5793

0.6179

0.6554

0.6915

0.7257

0.7580

0.7881 0.8159

0.8413

0.8643

0.8849

0.9032

0.9192

0.9332

0.9452

0.9554

0.9641

0.9713

0.9772

0.9821

0.9861

0.9893

0.9918

0.9938

0.9953

0.9965

0.9974

0.99810.5040

0.5438 0.5832

0.6217

0.6591

0.6950

0.7291

0.7611

0.7910

0.8186

0.8438

标准正态分布表 3

标准正态分布表

标准正态分布表（Standard Normal Distribution Table），也称为Z分数表或标准化分布表，是统计学中一个重要的参考工具。它提供了标准正态分布的累积概率密度函数值，使得我们可以通过查表的方式计算和获取不同Z分数对应的概率值。

标准正态分布是指均值为0，标准差为1的正态分布，其概率密度函数可以用公式表示为：

Φ(x) = 1 / √(2π) * e^(-x^2/2)，其中e为自然对数的底数，π为圆周率。

标准正态分布表的主要用途是帮助解决与正态分布有关的各种概率计算问题。通过查表，我们可以得到给定Z分数下的累积概率值，也可以根据给定概率值找到对应的Z分数。

标准正态分布表的构建方式是将标准正态分布的累积概率密度函数值进行离散化，然后整理成表格形式。一般而言，标准正态分布表的横轴是Z分数，纵轴是累积概率值。

下面是标准正态分布表的一个示例：

Z分数 0.00 0.01 0.02 0.03 ... 0.09

-3.4 0.0002 0.0003 0.0003 0.0003 ... 0.0004

-3.3 0.0005 0.0005 0.0006 0.0006 ... 0.0007 -3.2 0.0007 0.0008 0.0008 0.0009 ... 0.0010

-3.1 0.0010 0.0011 0.0011 0.0012 ... 0.0013

... ... ... ... ... ... ...

3.1 0.9989 0.9990 0.9990 0.9991 ... 0.9992

3.2 0.9991 0.9992 0.9992 0.9993 ... 0.9994

3.3 0.9993 0.9994 0.9994 0.9995 ... 0.9995

3.4 0.9995 0.9996 0.9996 0.9996 ... 0.9997

在实际应用中，我们可以通过以下步骤使用标准正态分布表：

标准正态分布表 4

标准正态分布表

φ( - x ) = 1 –φ( x )（请暂时忽略此公式）

x 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

0 0.500 0 0.504 0 0.508 0 0.512 0 0.516 0 0.519 9 0.523 9 0.527 9 0.531 9 0.535 9

0.1 0.539 8 0.543 8 0.547 8 0.551 7 0.555 7 0.559 6 0.563 6 0.567 5 0.571 4 0.575 3

0.2 0.579 3 0.583 2 0.587 1 0.591 0 0.594 8 0.598 7 0.602 6 0.606 4 0.610 3 0.614 1

0.3 0.617 9 0.621 7 0.625 5 0.629 3 0.633 1 0.636 8 0.640 4 0.644 3 0.648 0 0.651 7

0.4 0.655 4 0.659 1 0.662 8 0.666 4 0.670 0 0.673 6 0.677 2 0.680 8 0.684 4 0.687 9

0.5 0.691 5 0.695 0 0.698 5 0.701 9 0.705 4 0.708 8 0.712 3 0.715 7 0.719 0 0.722 4

0.6 0.725 7 0.729 1 0.732 4 0.735 7 0.738 9 0.742 2 0.745 4 0.748 6 0.751 7 0.754 9

0.7 0.758 0 0.761 1 0.764 2 0.767 3 0.770 3 0.773 4 0.776 4 0.779 4 0.782 3 0.785 2

0.8 0.788 1 0.791 0 0.793 9 0.796 7 0.799 5 0.802 3 0.805 1 0.807 8 0.810 6 0.813 3

标准正态分布表 5