Six Sigma Tool Navigator: The Master Guide for Teams

Table A: Proportions of Area Under the Normal Curve

How to use this table: Because the normal curve is symmetrical about a mean of zero (the left side being a mirror image of the right side), the areas corresponding to negative z-scores are identical to the areas of positive z-scores. For example, the areas corresponding to a z-score of - 1.00 are the same as those areas of a z-score of + 1.00. Z-scores are given in column A. Areas between (inside) the mean and the z-score are given in column B, and column C contains the area that lies beyond (outside) the z-score. And, since the curve is symmetric, each half of the curve contains .5000 of the total area.

Table A: Proportions of Area Under the Normal Curve

(A) Z

(B) area inside

& Z

(C) area outside Z

0.00

.0000

.5000

0.01

.0040

.4960

0.02

.0080

.4920

0.03

.0120

.4880

0.04

.0160

.4840

0.05

.0199

.4801

0.06

.0239

.4761

0.07

.0279

.4721

0.08

.0319

.4681

0.09

.0359

.4641

0.10

.0398

.4602

0.11

.0438

.4562

0.12

.0478

.4522

0.13

.0517

.4483

0.14

.0557

.4443

0.15

.0596

.4404

0.16

.0636

.4364

0.17

.0675

.4325

0.18

.0714

.4286

0.19

.0753

.4247

0.20

.0793

.4207

0.21

.0823

.4168

0.22

.0871

.4129

0.23

.0910

.4090

0.24

.0948

.4052

0.25

.0987

.4013

0.26

.1026

.3974

0.27

.1064

.3936

0.28

.1103

.3897

0.29

.1141

.3859

0.30

.1179

.3821

0.31

.1217

.3783

0.32

.1255

.3745

0.33

.1293

.3707

0.34

.1331

.3669

0.35

.1368

.3632

0.36

.1406

.3594

0.37

.1443

.3557

0.38

.1480

.3520

0.39

.1517

.3483

0.40

.1551

.3446

0.41

.1591

.3409

0.42

.1628

.3372

0.43

.1664

.3336

0.44

.1700

.3300

0.45

.1736

.3264

0.46

.1772

.3228

0.47

.1808

.3190

0.48

.1844

.3156

0.49

.1879

.3121

0.50

.1915

.3085

0.51

.1950

.3050

0.52

.1985

.3015

0.53

.2019

.2981

0.54

.2054

.2946

0.55

.2088

.2912

0.56

.2123

.2877

0.57

.2157

.2843

0.58

.2190

.2810

0.59

.2224

.2776

0.60

.2257

.2743

0.61

.2291

.2709

0.62

.2324

.2676

0.63

.2357

.2643

0.64

.2389

.2611

0.65

.2422

.2578

0.66

.2454

.2546

0.67

.2486

.2514

0.68

.2517

.2483

0.69

.2549

.2451

0.70

.2580

.2420

0.71

.2611

.2389

0.72

.2642

.2358

0.73

.2673

.2327

0.74

.2704

.2296

0.75

.2734

.2266

0.76

.2764

.2236

0.77

.2794

.2206

0.78

.2823

.2177

0.79

.2852

.2148

0.80

.2881

.2119

0.81

.2910

.2090

0.82

.2939

.2061

0.83

.2967

.2033

0.84

.2995

.2005

0.85

.3023

.1977

0.86

.3051

.1949

0.87

.3078

.1922

0.88

.3106

.1894

0.89

.3133

.1867

0.90

.3159

.1841

0.91

.3186

.1814

0.92

.3212

.1788

0.93

.3238

.1762

0.94

.3264

.1736

0.95

.3289

.1711

0.96

.3315

.1685

0.97

.3340

.1660

0.98

.3365

.1635

0.99

.3389

.1611

1.00

.3413

.1587

1.01

.3438

.1562

1.02

.3461

.1539

1.03

.3485

.1515

1.04

.3508

.1492

1.05

.3531

.1469

1.06

.3554

.1446

1.07

.3577

.1423

1.08

.3599

.1410

1.09

.3621

.1379

1.10

.3643

.1357

1.11

.3665

.1335

1.12

.3686

.1314

1.13

.3708

.1292

1.14

.3729

.1271

1.15

.3749

.1251

1.16

.3770

.1230

1.17

.3790

.1210

1.18

.3810

.1190

1.19

.3830

.1170

1.20

.3849

.1151

1.21

.3869

.1131

1.22

.3888

.1112

1.23

.3907

.1093

1.24

.3925

.1075

1.25

.3944

.1056

1.26

.3962

.1038

1.27

.3980

.1020

1.28

.3997

.1003

1.29

.4015

.0985

1.30

.4032

.0968

1.31

.4049

.0951

1.32

.4066

.0934

1.33

.4082

.0918

1.34

.4099

.0901

1.35

.4115

.0885

1.36

.4131

.0869

1.37

.4147

.0853

1.38

.4162

.0838

1.39

.4177

.0823

1.40

.4192

.0808

1.41

.4207

.0793

1.42

.4222

.0778

1.43

.4236

.0764

1.44

.4251

.0749

1.45

.4265

.0735

1.46

.4279

.0721

1.47

.4292

.0708

1.48

.4306

.0694

1.49

.4319

.0681

1.50

.4332

.0668

1.51

.4345

.0655

1.52

.4357

.0643

1.53

.4370

.0630

1.54

.4382

.0618

1.55

.4394

.0606

1.56

.4406

.0594

1.57

.4418

.0582

1.58

.4429

.0571

1.59

.4441

.0559

1.60

.4452

.0548

1.61

.4463

.0537

1.62

.4474

.0526

1.63

.4484

.0516

1.64

.4495

.0505

1.65

.4505

.0495

1.66

.4515

.0485

1.67

.4525

.0475

1.68

.4535

.0465

1.69

.4545

.0455

1.70

.4554

.0446

1.71

.4564

.0436

1.72

.4573

.0427

1.73

.4582

.0418

1.74

.4591

.0409

1.75

.4599

.0401

1.76

.4608

.0392

1.77

.4616

.0384

1.78

.4625

.0375

1.79

.4633

.0367

1.80

.4641

.0359

1.81

.4649

.0351

1.82

.4656

.0344

1.83

.4664

.0336

1.84

.4671

.0329

1.85

.4678

.0322

1.86

.4686

.0314

1.87

.4693

.0307

1.88

.4699

.0301

1.89

.4706

.0294

1.90

.4713

.0287

1.91

.4719

.0281

1.92

.4276

.0274

1.93

.4732

.0268

1.94

.4738

.0262

1.95

.4744

.0256

1.96

.4750

.0250

1.97

.4756

.0244

1.98

.4761

.0239

1.99

.4767

.0233

2.00

.4772

.0228

2.01

.4778

.0222

2.02

.4783

.0217

2.03

.4788

.0212

2.04

.4793

.0207

2.05

.4798

.0202

2.06

.4803

.0197

2.07

.4808

.0192

2.08

.4812

.0188

2.09

.4817

.0183

2.10

.4821

.0179

2.11

.4826

.0174

2.12

.4830

.0170

2.13

.4834

.0166

2.14

.4838

.0162

2.15

.4842

.0158

2.16

.4846

.0154

2.17

.4850

.0150

2.18

.4854

.0146

2.19

.4857

.0143

2.20

.4861

.0139

2.21

.4864

.0136

2.22

.4868

.0132

2.23

.4871

.0129

2.24

.4875

.0125

2.25

.4878

.0122

2.26

.4881

.0119

2.27

.4884

.0116

2.28

.4887

.0113

2.29

.4890

.0110

2.30

.4893

.0107

2.31

.4896

.0104

2.32

.4898

.0102

2.33

.4901

.0099

2.34

.4904

.0096

2.35

.4906

.0094

2.36

.4909

.0091

2.37

.4911

.0089

2.38

.4913

.0087

2.39

.4916

.0084

2.40

.4918

.0082

2.41

.4920

.0080

2.42

.4922

.0078

2.43

.4925

.0075

2.44

.4927

.0073

2.45

.4929

.0071

2.46

.4931

.0069

2.47

.4932

.0068

2.48

.4934

.0066

2.49

.4936

.0064

2.50

.4938

.0062

2.51

.4940

.0060

2.52

.4941

.0059

2.53

.4943

.0057

2.54

.4945

.0055

2.55

.4946

.0054

2.56

.4948

.0052

2.57

.4949

.0051

2.58

.4951

.0049

2.59

.4952

.0048

2.60

.4953

.0047

2.61

.4955

.0045

2.62

.4956

.0044

2.63

.4957

.0043

2.64

.4959

.0041

2.65

.4960

.0040

2.66

.4961

.0039

2.67

.4962

.0038

2.68

.4963

.0037

2.69

.4964

.0036

2.70

.4965

.0035

2.71

.4966

.0034

2.72

.4967

.0033

2.73

.4968

.0032

2.74

.4969

.0031

2.75

.4970

.0030

2.76

.4971

.0029

2.77

.4972

.0028

2.78

.4973

.0027

2.79

.4974

.0026

2.80

.4974

.0026

2.81

.4975

.0025

2.82

.4976

.0024

2.83

.4977

.0023

2.84

.4977

.0023

2.85

.4978

.0022

2.86

.4979

.0021

2.87

.4979

.0021

2.88

.4980

.0020

2.89

.4981

.0019

2.90

.4981

.0019

2.91

.4982

.0018

2.92

.4982

.0018

2.93

.4983

.0017

2.94

.4984

.0016

2.95

.4984

.0016

2.96

.4985

.0015

2.97

.4985

.0015

2.98

.4986

.0014

2.99

.4986

.0014

3.00

.4987

.0013

3.01

.4987

.0013

3.02

.4987

.0013

3.03

.4988

.0012

3.04

.4988

.0012

3.05

.4989

.0011

3.06

.4989

.0011

3.07

.4989

.001l

3.08

.4990

.0010

3.09

.4990

.0010

3.10

.4990

.0010

3.11

.4991

.0009

3.12

.4991

.0009

3.13

.4991

.0009

3.14

.4992

.0008

3.15

.4992

.0008

3.16

.4992

.0008

3.17

.4992

.0008

3.18

.4993

.0007

3.19

.4993

.0007

3.20

.4993

.0007

3.21

.4993

.0007

3.22

.4994

.0006

3.23

.4994

.0006

3.24

.4994

.0006

3.25

.4994

.0006

3.30

.4995

.0005

3.35

.4996

.0004

3.40

.4997

.0003

3.45

.4997

.0003

3.50

.4998

.0002

3.55

.4998

.0002

3.60

.4998

.0002

3.65

.4999

.0001

3.70

.4999

.0001

3.75

.4999

.0001

3.80

.4999

.0001

3.85

.4999

.0001

3.90

.49995

.00005

4.00

.49997

.00003

Critical values computed by John Timko. Used by permission.

Sigma(σ)

Centered

Shifted 1.5 σ

4.00

63[*]

99.9937[**]

6210[*]

99.379

5.00

0.57

99.999943

233

99.9767

6.00

0.002[†]

99.9999998

3.4[‡]

99.99966

[*]Defects per Million Opportunities (DPMO).

[**]% yield.

[†]At 6 σ, with a centered distribution (no variation shift), this figure is 2 defects per billion opportunities.

[‡]At 6 σ, with an off-centered distribution (Motorola's 1.5 σ long-term process variation shift average), is the often quoted statement "No more than 3.4 defects per million opportunities."

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