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15.3: Appendix C- The Z-Distribution Table

  • Page ID
    50193

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    The first column shows the positive version of each \(z\)-scores. The remaining columns report proportions in decimal form. The second column shows the proportion of scores from the \(z\)-score past the mean and to its furthest tail in the normal curve. The third column shows the proportion of scores from the \(z\)-score to its nearest tail of the normal curve. The fourth column shows the proportion of scores between the \(z\)-score and the mean (center) of the normal curve. To translate proportions to percents, multiply the proportion by 100.

    Recommendation: It can be easiest to identify which column(s) you need by using the sketch, shade, and solve method outlined in Chapter 5.

    Z-Score

    Proportion in the Body

    Proportion in the Tail

    Proportion between the Mean and the Z

    0.00

    0.5000

    0.5000

    0.0000

    0.01

    0.5040

    0.4960

    0.0040

    0.02

    0.5080

    0.4920

    0.0080

    0.03

    0.5120

    0.4880

    0.0120

    0.04

    0.5160

    0.4840

    0.0160

    0.05

    0.5199

    0.4801

    0.0199

    0.06

    0.5239

    0.4761

    0.0239

    0.07

    0.5279

    0.4721

    0.0279

    0.08

    0.5319

    0.4681

    0.0319

    0.09

    0.5359

    0.4641

    0.0359

    0.10

    0.5398

    0.4602

    0.0398

    0.11

    0.5438

    0.4562

    0.0438

    0.12

    0.5478

    0.4522

    0.0478

    0.13

    0.5517

    0.4483

    0.0517

    0.14

    0.5557

    0.4443

    0.0557

    0.15

    0.5596

    0.4404

    0.0596

    0.16

    0.5636

    0.4364

    0.0636

    0.17

    0.5675

    0.4325

    0.0675

    0.18

    0.5714

    0.4286

    0.0714

    0.19

    0.5753

    0.4247

    0.0753

    0.20

    0.5793

    0.4207

    0.0793

    0.21

    0.5832

    0.4168

    0.0832

    0.22

    0.5871

    0.4129

    0.0871

    0.23

    0.5910

    0.4090

    0.0910

    0.24

    0.5948

    0.4052

    0.0948

    0.25

    0.5987

    0.4013

    0.0987

    0.26

    0.6026

    0.3974

    0.1026

    0.27

    0.6064

    0.3936

    0.1064

    0.28

    0.6103

    0.3897

    0.1103

    0.29

    0.6141

    0.3859

    0.1141

    0.30

    0.6179

    0.3821

    0.1179

    0.31

    0.6217

    0.3783

    0.1217

    0.32

    0.6255

    0.3745

    0.1255

    0.33

    0.6293

    0.3707

    0.1293

    0.34

    0.6331

    0.3669

    0.1331

    0.35

    0.6368

    0.3632

    0.1368

    0.36

    0.6406

    0.3594

    0.1406

    0.37

    0.6443

    0.3557

    0.1443

    0.38

    0.6480

    0.3520

    0.1480

    0.39

    0.6517

    0.3483

    0.1517

    0.40

    0.6554

    0.3446

    0.1554

    0.41

    0.6591

    0.3409

    0.1591

    0.42

    0.6628

    0.3372

    0.1628

    0.43

    0.6664

    0.3336

    0.1664

    0.44

    0.6700

    0.3300

    0.1700

    0.45

    0.6736

    0.3264

    0.1736

    0.46

    0.6772

    0.3228

    0.1772

    0.47

    0.6808

    0.3192

    0.1808

    0.48

    0.6844

    0.3156

    0.1844

    0.49

    0.6879

    0.3121

    0.1879

    0.50

    0.6915

    0.3085

    0.1915

    0.51

    0.6950

    0.3050

    0.1950

    0.52

    0.6985

    0.3015

    0.1985

    0.53

    0.7019

    0.2981

    0.2019

    0.54

    0.7054

    0.2946

    0.2054

    0.55

    0.7088

    0.2912

    0.2088

    0.56

    0.7123

    0.2877

    0.2123

    0.57

    0.7157

    0.2843

    0.2157

    0.58

    0.7190

    0.2810

    0.2190

    0.59

    0.7224

    0.2776

    0.2224

    0.60

    0.7257

    0.2743

    0.2257

    0.61

    0.7291

    0.2709

    0.2291

    0.62

    0.7324

    0.2676

    0.2324

    0.63

    0.7357

    0.2643

    0.2357

    0.64

    0.7389

    0.2611

    0.2389

    0.65

    0.7422

    0.2578

    0.2422

    0.66

    0.7454

    0.2546

    0.2454

    0.67

    0.7486

    0.2514

    0.2486

    0.68

    0.7517

    0.2483

    0.2517

    0.69

    0.7549

    0.2451

    0.2549

    0.70

    0.7580

    0.2420

    0.2580

    0.71

    0.7611

    0.2389

    0.2611

    0.72

    0.7642

    0.2358

    0.2642

    0.73

    0.7673

    0.2327

    0.2673

    0.74

    0.7704

    0.2296

    0.2704

    0.75

    0.7734

    0.2266

    0.2734

    0.76

    0.7764

    0.2236

    0.2764

    0.77

    0.7794

    0.2206

    0.2794

    0.78

    0.7823

    0.2177

    0.2823

    0.79

    0.7852

    0.2148

    0.2852

    0.80

    0.7881

    0.2119

    0.2881

    0.81

    0.7910

    0.2090

    0.2910

    0.82

    0.7939

    0.2061

    0.2939

    0.83

    0.7967

    0.2033

    0.2967

    0.84

    0.7995

    0.2005

    0.2995

    0.85

    0.8023

    0.1977

    0.3023

    0.86

    0.8051

    0.1949

    0.3051

    0.87

    0.8078

    0.1922

    0.3078

    0.88

    0.8106

    0.1894

    0.3106

    0.89

    0.8133

    0.1867

    0.3133

    0.90

    0.8159

    0.1841

    0.3159

    0.91

    0.8186

    0.1814

    0.3186

    0.92

    0.8212

    0.1788

    0.3212

    0.93

    0.8238

    0.1762

    0.3238

    0.94

    0.8264

    0.1736

    0.3264

    0.95

    0.8289

    0.1711

    0.3289

    0.96

    0.8315

    0.1685

    0.3315

    0.97

    0.8340

    0.1660

    0.3340

    0.98

    0.8365

    0.1635

    0.3365

    0.99

    0.8389

    0.1611

    0.3389

    1.00

    0.8413

    0.1587

    0.3413

    1.01

    0.8438

    0.1562

    0.3438

    1.02

    0.8461

    0.1539

    0.3461

    1.03

    0.8485

    0.1515

    0.3485

    1.04

    0.8508

    0.1492

    0.3508

    1.05

    0.8531

    0.1469

    0.3531

    1.06

    0.8554

    0.1446

    0.3554

    1.07

    0.8577

    0.1423

    0.3577

    1.08

    0.8599

    0.1401

    0.3599

    1.09

    0.8621

    0.1379

    0.3621

    1.10

    0.8643

    0.1357

    0.3643

    1.11

    0.8665

    0.1335

    0.3665

    1.12

    0.8686

    0.1314

    0.3686

    1.13

    0.8708

    0.1292

    0.3708

    1.14

    0.8729

    0.1271

    0.3729

    1.15

    0.8749

    0.1251

    0.3749

    1.16

    0.8770

    0.1230

    0.3770

    1.17

    0.8790

    0.1210

    0.3790

    1.18

    0.8810

    0.1190

    0.3810

    1.19

    0.8830

    0.1170

    0.3830

    1.20

    0.8849

    0.1151

    0.3849

    1.21

    0.8869

    0.1131

    0.3869

    1.22

    0.8888

    0.1112

    0.3888

    1.23

    0.8907

    0.1093

    0.3907

    1.24

    0.8925

    0.1075

    0.3925

    1.25

    0.8944

    0.1056

    0.3944

    1.26

    0.8962

    0.1038

    0.3962

    1.27

    0.8980

    0.1020

    0.3980

    1.28

    0.8997

    0.1003

    0.3997

    1.29

    0.9015

    0.0985

    0.4015

    1.30

    0.9032

    0.0968

    0.4032

    1.31

    0.9049

    0.0951

    0.4049

    1.32

    0.9066

    0.0934

    0.4066

    1.33

    0.9082

    0.0918

    0.4082

    1.34

    0.9099

    0.0901

    0.4099

    1.35

    0.9115

    0.0885

    0.4115

    1.36

    0.9131

    0.0869

    0.4131

    1.37

    0.9147

    0.0853

    0.4147

    1.38

    0.9162

    0.0838

    0.4162

    1.39

    0.9177

    0.0823

    0.4177

    1.40

    0.9192

    0.0808

    0.4192

    1.41

    0.9207

    0.0793

    0.4207

    1.42

    0.9222

    0.0778

    0.4222

    1.43

    0.9236

    0.0764

    0.4236

    1.44

    0.9251

    0.0749

    0.4251

    1.45

    0.9265

    0.0735

    0.4265

    1.46

    0.9279

    0.0721

    0.4279

    1.47

    0.9292

    0.0708

    0.4292

    1.48

    0.9306

    0.0694

    0.4306

    1.49

    0.9319

    0.0681

    0.4319

    1.50

    0.9332

    0.0668

    0.4332

    1.51

    0.9345

    0.0655

    0.4345

    1.52

    0.9357

    0.0643

    0.4357

    1.53

    0.9370

    0.0630

    0.4370

    1.54

    0.9382

    0.0618

    0.4382

    1.55

    0.9394

    0.0606

    0.4394

    1.56

    0.9406

    0.0594

    0.4406

    1.57

    0.9418

    0.0582

    0.4418

    1.58

    0.9429

    0.0571

    0.4429

    1.59

    0.9441

    0.0559

    0.4441

    1.60

    0.9452

    0.0548

    0.4452

    1.61

    0.9463

    0.0537

    0.4463

    1.62

    0.9474

    0.0526

    0.4474

    1.63

    0.9484

    0.0516

    0.4484

    1.64

    0.9495

    0.0505

    0.4495

    1.65

    0.9505

    0.0495

    0.4505

    1.66

    0.9515

    0.0485

    0.4515

    1.67

    0.9525

    0.0475

    0.4525

    1.68

    0.9535

    0.0465

    0.4535

    1.69

    0.9545

    0.0455

    0.4545

    1.70

    0.9554

    0.0446

    0.4554

    1.71

    0.9564

    0.0436

    0.4564

    1.72

    0.9573

    0.0427

    0.4573

    1.73

    0.9582

    0.0418

    0.4582

    1.74

    0.9591

    0.0409

    0.4591

    1.75

    0.9599

    0.0401

    0.4599

    1.76

    0.9608

    0.0392

    0.4608

    1.77

    0.9616

    0.0384

    0.4616

    1.78

    0.9625

    0.0375

    0.4625

    1.79

    0.9633

    0.0367

    0.4633

    1.80

    0.9641

    0.0359

    0.4641

    1.81

    0.9649

    0.0351

    0.4649

    1.82

    0.9656

    0.0344

    0.4656

    1.83

    0.9664

    0.0336

    0.4664

    1.84

    0.9671

    0.0329

    0.4671

    1.85

    0.9678

    0.0322

    0.4678

    1.86

    0.9686

    0.0314

    0.4686

    1.87

    0.9693

    0.0307

    0.4693

    1.88

    0.9699

    0.0301

    0.4699

    1.89

    0.9706

    0.0294

    0.4706

    1.90

    0.9713

    0.0287

    0.4713

    1.91

    0.9719

    0.0281

    0.4719

    1.92

    0.9726

    0.0274

    0.4726

    1.93

    0.9732

    0.0268

    0.4732

    1.94

    0.9738

    0.0262

    0.4738

    1.95

    0.9744

    0.0256

    0.4744

    1.96

    0.9750

    0.0250

    0.4750

    1.97

    0.9756

    0.0244

    0.4756

    1.98

    0.9761

    0.0239

    0.4761

    1.99

    0.9767

    0.0233

    0.4767

    2.00

    0.9772

    0.0228

    0.4772

    2.01

    0.9778

    0.0222

    0.4778

    2.02

    0.9783

    0.0217

    0.4783

    2.03

    0.9788

    0.0212

    0.4788

    2.04

    0.9793

    0.0207

    0.4793

    2.05

    0.9798

    0.0202

    0.4798

    2.06

    0.9803

    0.0197

    0.4803

    2.07

    0.9808

    0.0192

    0.4808

    2.08

    0.9812

    0.0188

    0.4812

    2.09

    0.9817

    0.0183

    0.4817

    2.10

    0.9821

    0.0179

    0.4821

    2.11

    0.9826

    0.0174

    0.4826

    2.12

    0.9830

    0.0170

    0.4830

    2.13

    0.9834

    0.0166

    0.4834

    2.14

    0.9838

    0.0162

    0.4838

    2.15

    0.9842

    0.0158

    0.4842

    2.16

    0.9846

    0.0154

    0.4846

    2.17

    0.9850

    0.0150

    0.4850

    2.18

    0.9854

    0.0146

    0.4854

    2.19

    0.9857

    0.0143

    0.4857

    2.20

    0.9861

    0.0139

    0.4861

    2.21

    0.9864

    0.0136

    0.4864

    2.22

    0.9868

    0.0132

    0.4868

    2.23

    0.9871

    0.0129

    0.4871

    2.24

    0.9875

    0.0125

    0.4875

    2.25

    0.9878

    0.0122

    0.4878

    2.26

    0.9881

    0.0119

    0.4881

    2.27

    0.9884

    0.0116

    0.4884

    2.28

    0.9887

    0.0113

    0.4887

    2.29

    0.9890

    0.0110

    0.4890

    2.30

    0.9893

    0.0107

    0.4893

    2.31

    0.9896

    0.0104

    0.4896

    2.32

    0.9898

    0.0102

    0.4898

    2.33

    0.9901

    0.0099

    0.4901

    2.34

    0.9904

    0.0096

    0.4904

    2.35

    0.9906

    0.0094

    0.4906

    2.36

    0.9909

    0.0091

    0.4909

    2.37

    0.9911

    0.0089

    0.4911

    2.38

    0.9913

    0.0087

    0.4913

    2.39

    0.9916

    0.0084

    0.4916

    2.40

    0.9918

    0.0082

    0.4918

    2.41

    0.9920

    0.0080

    0.4920

    2.42

    0.9922

    0.0078

    0.4922

    2.43

    0.9925

    0.0075

    0.4925

    2.44

    0.9927

    0.0073

    0.4927

    2.45

    0.9929

    0.0071

    0.4929

    2.46

    0.9931

    0.0069

    0.4931

    2.47

    0.9932

    0.0068

    0.4932

    2.48

    0.9934

    0.0066

    0.4934

    2.49

    0.9936

    0.0064

    0.4936

    2.50

    0.9938

    0.0062

    0.4938

    2.51

    0.9940

    0.0060

    0.4940

    2.52

    0.9941

    0.0059

    0.4941

    2.53

    0.9943

    0.0057

    0.4943

    2.54

    0.9945

    0.0055

    0.4945

    2.55

    0.9946

    0.0054

    0.4946

    2.56

    0.9948

    0.0052

    0.4948

    2.57

    0.9949

    0.0051

    0.4949

    2.58

    0.9951

    0.0049

    0.4951

    2.59

    0.9952

    0.0048

    0.4952

    2.60

    0.9953

    0.0047

    0.4953

    2.61

    0.9955

    0.0045

    0.4955

    2.62

    0.9956

    0.0044

    0.4956

    2.63

    0.9957

    0.0043

    0.4957

    2.64

    0.9959

    0.0041

    0.4959

    2.65

    0.9960

    0.0040

    0.4960

    2.66

    0.9961

    0.0039

    0.4961

    2.67

    0.9962

    0.0038

    0.4962

    2.68

    0.9963

    0.0037

    0.4963

    2.69

    0.9964

    0.0036

    0.4964

    2.70

    0.9965

    0.0035

    0.4965

    2.71

    0.9966

    0.0034

    0.4966

    2.72

    0.9967

    0.0033

    0.4967

    2.73

    0.9968

    0.0032

    0.4968

    2.74

    0.9969

    0.0031

    0.4969

    2.75

    0.9970

    0.0030

    0.4970

    2.76

    0.9971

    0.0029

    0.4971

    2.77

    0.9972

    0.0028

    0.4972

    2.78

    0.9973

    0.0027

    0.4973

    2.79

    0.9974

    0.0026

    0.4974

    2.80

    0.9974

    0.0026

    0.4974

    2.81

    0.9975

    0.0025

    0.4975

    2.82

    0.9976

    0.0024

    0.4976

    2.83

    0.9977

    0.0023

    0.4977

    2.84

    0.9977

    0.0023

    0.4977

    2.85

    0.9978

    0.0022

    0.4978

    2.86

    0.9979

    0.0021

    0.4979

    2.87

    0.9979

    0.0021

    0.4979

    2.88

    0.9980

    0.0020

    0.4980

    2.89

    0.9981

    0.0019

    0.4981

    2.90

    0.9981

    0.0019

    0.4981

    2.91

    0.9982

    0.0018

    0.4982

    2.92

    0.9982

    0.0018

    0.4982

    2.93

    0.9983

    0.0017

    0.4983

    2.94

    0.9984

    0.0016

    0.4984

    2.95

    0.9984

    0.0016

    0.4984

    2.96

    0.9985

    0.0015

    0.4985

    2.97

    0.9985

    0.0015

    0.4985

    2.98

    0.9986

    0.0014

    0.4986

    2.99

    0.9986

    0.0014

    0.4986

    3.00

    0.9987

    0.0013

    0.4987

    3.01

    0.9987

    0.0013

    0.4987

    3.02

    0.9987

    0.0013

    0.4987

    3.03

    0.9988

    0.0012

    0.4988

    3.04

    0.9988

    0.0012

    0.4988

    3.05

    0.9989

    0.0011

    0.4989

    3.06

    0.9989

    0.0011

    0.4989

    3.07

    0.9989

    0.0011

    0.4989

    3.08

    0.9990

    0.0010

    0.4990

    3.09

    0.9990

    0.0010

    0.4990

    3.10

    0.9990

    0.0010

    0.4990

    3.11

    0.9991

    0.0009

    0.4991

    3.12

    0.9991

    0.0009

    0.4991

    3.13

    0.9991

    0.0009

    0.4991

    3.14

    0.9992

    0.0008

    0.4992

    3.15

    0.9992

    0.0008

    0.4992

    3.16

    0.9992

    0.0008

    0.4992

    3.17

    0.9992

    0.0008

    0.4992

    3.18

    0.9993

    0.0007

    0.4993

    3.19

    0.9993

    0.0007

    0.4993

    3.20

    0.9993

    0.0007

    0.4993

    3.21

    0.9993

    0.0007

    0.4993

    3.22

    0.9994

    0.0006

    0.4994

    3.23

    0.9994

    0.0006

    0.4994

    3.24

    0.9994

    0.0006

    0.4994

    3.25

    0.9994

    0.0006

    0.4994

    3.26

    0.9994

    0.0006

    0.4994

    3.27

    0.9995

    0.0005

    0.4995

    3.28

    0.9995

    0.0005

    0.4995

    3.29

    0.9995

    0.0005

    0.4995

    3.30

    0.9995

    0.0005

    0.4995

    3.31

    0.9995

    0.0005

    0.4995

    3.32

    0.9995

    0.0005

    0.4995

    3.33

    0.9996

    0.0004

    0.4996

    3.34

    0.9996

    0.0004

    0.4996

    3.35

    0.9996

    0.0004

    0.4996

    3.36

    0.9996

    0.0004

    0.4996

    3.37

    0.9996

    0.0004

    0.4996

    3.38

    0.9996

    0.0004

    0.4996

    3.39

    0.9997

    0.0003

    0.4997

    3.40

    0.9997

    0.0003

    0.4997

    3.41

    0.9997

    0.0003

    0.4997

    3.42

    0.9997

    0.0003

    0.4997

    3.43

    0.9997

    0.0003

    0.4997

    3.44

    0.9997

    0.0003

    0.4997

    3.45

    0.9997

    0.0003

    0.4997

    3.46

    0.9997

    0.0003

    0.4997

    3.47

    0.9997

    0.0003

    0.4997

    3.48

    0.9997

    0.0003

    0.4997

    3.49

    0.9998

    0.0002

    0.4998

    3.50

    0.9998

    0.0002

    0.4998

    3.51

    0.9998

    0.0002

    0.4998

    3.52

    0.9998

    0.0002

    0.4998

    3.53

    0.9998

    0.0002

    0.4998

    3.54

    0.9998

    0.0002

    0.4998

    3.55

    0.9998

    0.0002

    0.4998

    3.56

    0.9998

    0.0002

    0.4998

    3.57

    0.9998

    0.0002

    0.4998

    3.58

    0.9998

    0.0002

    0.4998

    3.59

    0.9998

    0.0002

    0.4998

    3.60

    0.9998

    0.0002

    0.4998

    3.61

    0.9998

    0.0002

    0.4998

    3.62

    0.9999

    0.0001

    0.4999

    3.63

    0.9999

    0.0001

    0.4999

    3.64

    0.9999

    0.0001

    0.4999

    3.65

    0.9999

    0.0001

    0.4999

    3.66

    0.9999

    0.0001

    0.4999

    3.67

    0.9999

    0.0001

    0.4999

    3.68

    0.9999

    0.0001

    0.4999

    3.69

    0.9999

    0.0001

    0.4999

    3.70

    0.9999

    0.0001

    0.4999

    3.71

    0.9999

    0.0001

    0.4999

    3.72

    0.9999

    0.0001

    0.4999

    3.73

    0.9999

    0.0001

    0.4999

    3.74

    0.9999

    0.0001

    0.4999

    3.75

    0.9999

    0.0001

    0.4999

    3.76

    0.9999

    0.0001

    0.4999

    3.77

    0.9999

    0.0001

    0.4999

    3.78

    0.9999

    0.0001

    0.4999

    3.79

    0.9999

    0.0001

    0.4999

    3.80

    0.9999

    0.0001

    0.4999

    3.81

    0.9999

    0.0001

    0.4999

    3.82

    0.9999

    0.0001

    0.4999

    3.83

    0.9999

    0.0001

    0.4999

    3.84

    0.9999

    0.0001

    0.4999

    3.85

    0.9999

    0.0001

    0.4999

    3.86

    0.9999

    0.0001

    0.4999

    3.87

    0.9999

    0.0001

    0.4999

    3.88

    0.9999

    0.0001

    0.4999

    3.89

    0.9999

    0.0001

    0.4999

    3.90

    1.0000

    0.0000

    0.5000

    3.91

    1.0000

    0.0000

    0.5000

    3.92

    1.0000

    0.0000

    0.5000

    3.93

    1.0000

    0.0000

    0.5000

    3.94

    1.0000

    0.0000

    0.5000

    3.95

    1.0000

    0.0000

    0.5000

    3.96

    1.0000

    0.0000

    0.5000

    3.97

    1.0000

    0.0000

    0.5000

    3.98

    1.0000

    0.0000

    0.5000

    3.99

    1.0000

    0.0000

    0.5000

    4.00

    1.0000

    0.0000

    0.5000



    This page titled 15.3: Appendix C- The Z-Distribution Table is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by .

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