Appendix C: Statistical Tables


Table I: Normal Distribution”Area under the Curve

z

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.0

5.00E-01

4.96E-01

4.92E-01

4.88E-01

4.84E-01

4.80E-01

4.76E-01

4.72E-01

4.68E-01

4.64E-01

0.1

4.60E-01

4.56E-01

4.52E-01

4.48E-01

4.44E-01

4.40E-01

4.36E-01

4.33E-01

4.29E-01

4.25E-01

0.2

4.21E-01

4.17E-01

4.13E-01

4.09E-01

4.05E-01

4.01E-01

3.97E-01

3.94E-01

3.90E-01

3.86E-01

0.3

3.82E-01

3.78E-01

3.75E-01

3.71E-01

3.67E-01

3.63E-01

3.59E-01

3.56E-01

3.52E-01

3.48E-01

0.4

3.45E-0I

3.41E-01

3.37E-01

3.34E-01

3.30E-01

3.26E-01

3.23E-01

3.19E-01

3.16E-01

3.12E-01

0.5

3.09E-01

3.05E-01

3.02E-01

2.98E-01

2.95E-01

2.91E-01

2.88E-01

2.84E-01

2.81E-01

2.78E-01

0.6

2.74E-01

2.71E-01

2.68E-01

2.64E-01

2.61E-01

2.58E-01

2.55E-01

2.51E-01

2.48E-01

2.45E-01

0.7

2.42E-01

2.39E-01

2.36E-01

2.33E-01

2.30E-01

2.27E-01

2.24E-01

2.21E-01

2.18E-01

2.15E-01

0.8

2.12E-01

2.09E-01

2.06E-01

2.03E-01

2.01E-01

1.98E-01

1.95E-01

1.92E-01

1.89E-01

1.87E-01

0.9

1.84E-01

1.81E-01

1.79E-01

1.76E-01

1.74E-01

1.71E-01

1.69E-01

1.66E-01

1.64E-01

1.61E-01

1.0

I.59E-01

1.56E-01

1.59E-01

1.52E-01

1.49E-01

1.47E-01

1.45E-01

1.42E-01

1.40E-01

1.38E-01

1.1

1.36E-01

1.34E-01

1.31E-01

1.29E-01

1.27E-01

1.25E-01

1.23E-01

1.21E-01

1.19E-01

1.17E-01

1.2

1.15E-01

1.13E-01

1.11E-01

1.09E-01

1.08E-01

1.06E-01

1.04E-01

1.02E-01

1.00E-01

9.85E-02

1.3

9.68E-02

9.51E-02

9.34E-02

9.18E-02

9.01E-02

8.85E-02

8.69E-02

8.53E-02

8.38E-02

8.23E-02

1.4

8.08E-02

7.93E-02

7.78E-02

7.64E-02

7.49E-02

7.35E-02

7.21E-02

7.08E-02

6.94E-02

6.81E-02

1.5

6.68E-02

6.55E-02

6.43E-02

6.30E-02

6.18E-02

6.06E-02

5.94E-02

5.82E-02

5.71E-02

5.59E-02

1.6

5.48E-02

5.37E-02

5.26E-02

5.16E-02

5.05E-02

4.95E-02

4.85E-02

4.75E-02

4.65E-02

4.55E-02

1.7

4.46E-02

4.36E-02

4.27E-02

4.18E-02

4.09E-02

4.01E-02

3.92E-02

3.84E-02

3.75E-02

3.67E-02

1.8

3.59E-02

3.52E-02

3.44E-02

3.36E-02

3.29E-02

3.22E-02

3.14E-02

3.07E-02

3.01E-02

2.94E-02

1.9

2.87E-02

2.81E-02

2.74E-02

2.68E-02

2.62E-02

2.56E-02

2.50E-02

2.44E-02

2.39E-02

2.33E-02

2.0

2.28E-02

2.22E-02

2.17E-02

2.12E-02

2.07E-02

2.02E-02

1.97E-02

1.92E-02

1.88E-02

1.83E-02

2.1

L.79E-02

1.74E-02

1.70E-02

1.66E-02

1.62E-02

1.58E-02

1.54E-02

1.50E-02

1.46E-02

1.43E-02

2.2

1.39E-02

1.36E-02

1.32E-02

1.29E-02

1.26E-02

1.22E-02

1.19E-02

1.16E-02

1.13E-02

1.10E-02

2.3

1.07E-02

1.04E-02

1.02E-02

9.90E-03

9.64E-03

9.39E-03

9.14E-03

8.89E-03

8.66E-03

8.42E-03

2.4

8.20E-03

7.98E-03

7.76E-03

7.55E-03

7.34E-03

7.14E-03

6.95E-03

6.76E-03

6.57E-03

6.39E-03

2.5

6.21E-03

6.04E-03

5.87E-03

5.70E-03

5.54E-03

5.39E-03

5.23E-03

5.09E-03

4.94E-03

4.80E-03

2.6

4.66E-03

4.53E-03

4.40E-03

4.27E-03

4.15E-03

4.02E-03

3.91E-03

3.79E-03

3.68E-03

3.57E-03

2.7

3.47E-03

3.36E-03

3.26E-03

3.17E-03

3.07E-03

2.98E-03

2.89E-03

2.80E-03

2.72E-03

2.64E-03

2.8

2.56E-03

2.48E-03

2.40E-03

2.33E-03

2.26E-03

2.19E-03

2.12E-03

2.05E-03

1.99E-03

1.93E-03

2.9

1.87E-03

1.81E-03

1.75E-03

1.70E-03

1.64E-03

1.59E-03

1.54E-03

1.49E-03

1.44E-03

1.40E-03

3.0

1.35E-03

1.31E-03

1.26E-03

1.22E-03

1.18E-03

1.14E-03

1.11E-03

1.07E-03

1.04E-03

1.00E-03

3.1

9.68E-04

9.35E-04

9.04E-04

8.74E-04

8.45E-04

8.16E-04

7.89E-04

7.62E-04

7.36E-04

7.11E-04

3.2

6.87E-04

6.64E-04

6.41E-04

6.19E-04

5.98E-04

5.77E-04

5.57E-04

5.38E-04

5.19E-04

5.01E-04

3.3

4.84E-04

4.67E-04

4.50E-04

4.34E-04

4.19E-04

4.04E-04

3.90E-04

3.76E-04

3.63E-04

3.50E-04

3.4

3.37E-04

3.25E-04

3.13E-04

3.02E-04

2.91E-04

2.80E-04

2.70E-04

2.60E-04

2.51E-04

2.42E-04

3.5

2.33E-04

2.24E-04

2.16E-04

2.08E-04

2.00E-04

1.93E-04

1.86E-04

1.79E-04

1.72E-04

1.66E-04

3.6

1.59E-04

1.53E-04

1.47E-04

1.42E-04

1.36E-04

1.31E-04

1.26E-04

1.21E-04

1.17E-04

1.12E-04

3.7

1.08E-04

1.04E-04

9.97E-05

9.59E-05

9.21E-05

8.86E-05

8.51E-05

8.18E-05

7.85E-05

7.55E-05

3.8

7.25E-05

6.96E-05

6.69E-05

6.42E-05

6.17E-05

5.92E-05

5.68E-05

5.46E-05

5.24E-05

5.03E-05

3.9

4.82E-05

4.63E-05

4.44E-05

4.26E-05

4.09E-05

3.92E-05

3.76E-05

3.61E-05

3.46E-05

3.32E-05

4.0

3.18E-05

3.05E-05

2.92E-05

2.80E-05

2.68E-05

2.57E-05

2.47E-05

2.36E-05

2.26E-05

2.17E-05

4.1

2.08E-05

1.99E-05

1.91E-05

1.82E-05

1.75E-05

1.67E-05

1.60E-05

1.53E-05

1.47E-05

1.40E-05

4.2

1.34E-05

1.29E-05

1.23E-05

1.18E-05

1.13E-05

1.08E-05

1.03E-05

9.86E-06

9.43E-06

9.0IE-06

4.3

8.62E-06

8.24E-06

7.88E-06

7.53E-06

7.20E-06

6.88E-06

6.57E-06

6.28E-06

6.00E-06

5.73E-06

4.4

5.48E-06

5.23E-06

5.00E-06

4.77E-06

4.56E-06

4.35E-06

4.16E-06

3.97E-06

3.79E-06

3.62E-06

4.5

3.45E-06

3.29E-06

3.14E-06

3.00E-06

2.86E-06

2.73E-06

2.60E-06

2.48E-06

2.37E-06

2.26E-06

4.6

2.15E-06

2.05E-06

1.96E-06

1.87E-06

1.78E-06

1.70E-06

1.62E-06

1.54E-06

1.47E-06

1.40E-06

4.7

1.33E-06

1.27E-06

1.21E-06

1.15E-06

1.10E-06

1.05E-06

9.96E-07

9.48E-07

9.03E-07

8.59E-07

4.8

8.18E-07

7.79E-07

7.41E-07

7.05E-07

6.71E-07

6.39E-07

6.08E-07

5.78E-07

5.50E-07

5.23E-07

4.9

4.98E-07

4.73E-07

4.50E-07

4.28E-07

4.07E-07

3.87E-07

3.68E-07

3.50E-07

3.32E-07

3.16E-07

5.0

3.00E-07

2.85E-07

2.71E-07

2.58E-07

2.45E-07

2.32E-07

2.21E-07

2.10E-07

1.99E-07

1.89E-07

5.1

1.80E-07

1.71E-07

1.62E-07

1.54E-07

1.46E-07

1.39E-07

1.31E-07

1.25E-07

1.18E-07

1.12E-07

5.2

1.07E-07

1.01E-07

9.59E-08

9.10E-08

8.63E-08

8.18E-08

7.76E-08

7.36E-08

6.98E-08

6.62E-08

5.3

6.27E-08

5.95E-08

5.64E-08

5.34E-08

5.06E-08

4.80E-08

4.55E-08

4.31E-08

4.08E-08

3.87E-08

5.4

3.66E-08

3.47E-08

3.29E-08

3.11E-08

2.95E-08

2.79E-08

2.64E-08

2-50E-08

2.37E-08

2.24E-08

5.5

2.12E-08

2.01E-08

1.90E-08

1.80E-08

1.70E-08

1.61E-08

1.53E-08

1.44E-08

1.37E-08

1.29E-08

5.6

1.22E-08

1.16E-08

1.09E-08

1.03E-08

9.78E-09

9.24E-09

8.74E-09

8.26E-09

7.81E-09

7,39E-09

5.7

6.98E-09

6.60E-09

6.24E-09

5.89E-09

5.57E-09

5.26E-09

4.97E-09

4.70E-09

4.44E-09

4.19E-09

5.8

3.96E-09

3.74E-09

3.53E-09

3.34E-09

3.15E-09

2.97E-09

2.81E-09

2.65E-09

2.50E-09

2.36E-09

5.9

2.23E-09

2.11E-09

1.99E-09

1.88E-09

1.77E-09

1.67E-09

1.58E-09

1.49E-09

1.40E-09

1.32E-09

6.0

1.25E-09

1.18E-09

1.11E-09

1.05E-09

9.88E-10

9.31E-10

8.78E-10

8.28E-10

7.81E-10

7.36E-10

6.1

6.94E-10

6.54E-10

6.17E-10

5.81E-10

5.48E-10

5.16E-10

4.87E-10

4.59E-10

4.32E-10

4.07E-10

6.2

3.84E-10

3.61E-10

3.40E-10

3.21E-10

3.02E-10

2.84E-10

2.68E-10

2.52E-10

2.38E-10

2.24E-10

6.3

2.11E-10

1.98E-10

1.87E-10

1.76E-10

1.66E-10

1.56E-10

1.47E-10

1.38E-10

1:30E-10

1.22E-10

6.4

1.15E-10

1.08E-10

1.02E-10

9.59E-11

9.02E-11

8.49E-11

7.98E-11

7.51E-11

7:06E-11

6.65E-11

6.5

6.25E-11

5.88E-11

5.53E-11

5.20E-11

4.89E-11

4.60E-11

4.32E-11

4.07E-11

3.82E-11

3.59E-11

6.6

3.38E-11

3.18E-11

2.98E-11

2.81E-11

2.64E-11

2.48E-11

2.33E-11

2.19E-11

2.06E-11

1.93E-11

6.7

1.82E-11

1.71E-11

1.60E-11

1.51E-11

1.42E-11

1.33E-11

1.25E-11

1.17E-11

1.10E-11

1.04E-11

6.8

9.72E-12

9.13E-12

8.57E-12

8.05E-12

7.56E-12

7.10E-12

6.66E-12

6.26E-12

5.87E-12

5.52E-12

6.9

5.18E-12

4.86E-12

4.56E-12

4.28E-12

4.02E-12

3.77E-12

3.54E-12

3.32E-12

3.12E-12

2.93E-12

7.0

2.75E-12

2.58E-12

2.42E-12

2.27E-12

2.13E-12

2.00E-12

1.87E-12

1.76E-12

1.65E-12

1.55E-12

7.1

1.45E-12

1.36E-12

1.28E-12

1.20E-12

1.12E-12

1.05E-12

9.88E-13

9.26E-13

8.69E-13

8.15E-13

7.2

7.64E-13

7.16E-13

6.72E-13

6.30E-13

5.90E-13

5.54E-13

5.19E-13

4.86E-13

4.56E-13

4.28E-13

7.3

4.01E-13

3.76E-13

3.52E-13

3.30E-13

3.09E-13

2.90E-13

2.72E-13

2.55E-13

2.39E-13

2.24E-13

7.4

2.10E-13

1.96E-13

1.84E-13

1.72E-13

1.62E-13

1.51E-13

1.42E-13

1.33E-13

1.24E-13

1.17E-13

7.5

1.09E-13

1.02E-13

9.58E-14

8.98E-14

8.41E-14

7.87E-14

7.38E-14

6.91E-14

6.47E-14

6.06E-14

7.6

5.68E-14

5.32E-14

4.98E-14

4.66E-14

4.37E-14

4.09E-14

3.83E-14

3.58E-14

3.36E-14

3.14E-14

7.7

2.94E-14

2.76E-14

2.58E-14

2.42E-14

2.26E-14

2.12E-14

1.98E-14

1.86E-14

1.74E-14

1.63E-14

7.8

1.52E-14

1.42E-14

1.33E-14

1.25E-14

1.17E-14

1.09E-14

1.02E-14

9.58E-15

8.97E-15

8.39E-15

7.9

7.85E-15

7.35E-15

6.88E-15

6.44E-15

6.02E-15

5.64E-15

5.28E-15

4.94E-15

4.62E-15

4.32E-15

8.0

4.05E-15

3.79E-15

3.54E-15

3.31E-15

3.10E-15

2.90E-15

2.72E-15

2.54E-15

2.38E-15

2.22E-15

8.1

2.08E-15

1.95E-15

1.82E-15

1.70E-15

1.59E-15

1.49E-15

1.40E-15

1.31E-15

1.22E-15

1.14E-15

8.2

1.07E-15

9.99E-16

9.35E-16

8.74E-16

8.18E-16

7.65E-16

7.16E-16

6.69E-16

6.26E-16

5.86E-16

8.3

5.48E-16

5.12E-16

4.79E-16

4.48E-16

4.19E-16

3.92E-16

3.67E-16

3.43E-16

3.21E-16

3.00E-16

8.4

2.81E-16

2.62E-16

2.45E-16

2.30E-16

2.15E-16

2.01E-16

1.88E-16

1.76E-16

1.64E-16

1.54E-16

8.5

1.44E-16

1.34E-16

1.26E-16

1.17E-16

1.10E-16

1.03E-16

9.60E-17

8.98E-17

8.40E-17

7.85E-17

8.6

7.34E-17

6.87E-17

6.42E-17

6.00E-17

5.61E-17

5.25E-17

4.91E-17

4.59E-17

4.29E-17

4.01E-17

8.7

3.75E-17

3.51E-17

3.28E-17

3.07E-17

2.87E-17

2.68E-17

2.51E-17

2.35E-17

2.19E-17

2.05E-17

8.8

1.92E-17

1.79E-17

1.68E-17

1.57E-17

1.47E-17

1.37E-17

1.28E-17

1.20E-17

1.12E-17

1.05E-17

8.9

9.79E-18

9.16E-18

8.56E-18

8.00E-18

7.48E-18

7.00E-18

6.54E-18

6.12E-18

5.72E-18

5.35E-18

9.0

5.00E-18

4.68E-18

4.37E-18

4.09E-18

3.82E-18

3.57E-18

3.34E-18

3.13E-18

2.92E-18

2.73E-18

9.1

2.56E-18

2.39E-18

2.23E-18

2.09E-18

1.95E-18

1.83E-18

1.71E-18

1.60E-18

1.49E-18

1.40E-18

9.2

1.31E-18

1.22E-18

1.14E-18

1.07E-18

9.98E-19

9.33E-19

8.73E-19

8.16E-19

7.63E-19

7.14E-19

9.3

6.67E-19

6.24E-19

5.83E-19

5.46E-19

5.10E-19

4.77E-19

4.46E-19

4.17E-19

3.90E-19

3.65E-19

9.4

3.41E-19

3.19E-19

2.98E-19

2.79E-19

2.61E-19

2.44E-19

2.28E-19

2.14E-19

2.00E-19

1.87E-19

9.5

1.75E-19

1.63E-19

1.53E-19

1.43E-19

1.34E-19

1.25E-19

1.17E-19

1.09E-19

1.02E-19

9.56E-20

9.6

8.94E-20

8.37E-20

7.82E-20

7.32E-20

6.85E-20

6.40E-20

5.99E-20

5.60E-20

5.24E-20

4.90E-20

9.7

4.58E-20

4.29E-20

4.01E-20

3.75E-20

3.51E-20

3.28E-20

3.07E-20

2.87E-20

2.69E-20

2.52E-20

9.8

2.35E-20

2.20E-20

2.06E-20

1.93E-20

1.80E-20

1.69E-20

1.58E-20

1.48E-20

1.38E-20

1.29E-20

9.9

1.21E-20

1.13E-20

1.06E-20

9.90E-21

9.26E-21

8.67E-21

8.11E-21

7.59E-21

7.10E-21

6.64E-21

10.0

6.22E-21

5.82E-21

5.44E-21

5.09E-21

4.77E-21

4.46E-21

4.17E-21

3.91E-21

3.66E-21

3.42E-21

Table II: The t Distribution
 

.600

.700

.800

.900

.950

.975

.990

.995

1

0.325

0.727

1.376

3.078

6.314

12.706

31.821

63.657

2

0.289

0.617

1.061

1.886

2.920

4.303

6.965

9.925

3

0.277

0.584

0.978

1.638

2.353

3.182

4.541

5.841

4

0.271

0.569

0.941

1.533

2.132

2.776

3.747

4.604

5

0.267

0.559

0.920

1.476

2.015

2.571

3.365

4.032

6

0.265

0.553

0.906

1.440

1.943

2.447

3.143

3.707

7

0.263

0.549

0.896

1.415

1.895

2.365

2.998

3.499

8

0.262

0.546

0.889

1.397

1.860

2.306

2.896

3.355

9

0.261

0.543

0.883

1.383

1.833

2.262

2.821

3.250

10

0.260

0.542

0.879

1.372

1.812

2.228

2.764

3.169

11

0.260

0.540

0.876

1.363

1.796

2.201

2.718

3.106

12

0.259

0.539

0.873

1.356

1.782

2.179

2.681

3.055

13

0.259

0.538

0.870

1.350

1.771

2.160

2.650

3.012

14

0.258

0.537

0.868

1.345

1.761

2.145

2.624

2.977

15

0.258

0.536

0.866

1.341

1.753

2.131

2.602

2.947

16

0.258

0.535

0.865

1.337

1.746

2.120

2.583

2.921

17

0.257

0.534

0.863

1.333

1.740

2.110

2.567

2.898

18

0.257

0.534

0.862

1.330

1.734

2.101

2.552

2.878

19

0.257

0.533

0.861

1.328

1.729

2.093

2.539

2.861

20

0.257

0.533

0.860

1.325

1.725

2.086

2.528

2.845

21

0.257

0.532

0.859

1.323

1.721

2.080

2.518

2.831

22

0.256

0.532

0.858

1.321

1.717

2.074

2.508

2.819

23

0.256

0.532

0.858

1.319

1.714

2.069

2.500

2.807

24

0.256

0.531

0.857

1.318

1.711

2.064

2.492

2.797

25

0.256

0.531

0.856

1.316

1.708

2.060

2.485

2.787

26

0.256

0.531

0.856

1.315

1.706

2.056

2.479

2.779

27

0.256

0.531

0.855

1.314

1.703

2.052

2.473

2.771

28

0.256

0.530

0.855

1.313

1.701

2.048

2.467

2.763

29

0.256

0.530

0.854

1.311

1.699

2.045

2.462

2.756

30

0.256

0.530

0.854

1.310

1.697

2.042

2.457

2.750

40

0.255

0.529

0.851

1.303

1.684

2.021

2.423

2.704

60

0.254

0.527

0.848

1.296

1.671

2.000

2.390

2.660

120

0.254

0.526

0.845

1.289

1.658

1.980

2.358

2.617

ˆ

0.253

0.524

0.842

1.282

1.645

1.960

2.326

2.576

Table III: Chi Square ( X 2 ) Distribution

df

.995

.990

.975

.950

.900

.750

.500

1

.000039

.000160

.000980

.003930

.015800

.101500

.455000

2

0.010

0.020

0.051

0.103

0.211

0.575

1.386

3

0.072

0.115

0.216

0.352

0.584

1.213

2.366

4

0.201

0.297

0.484

0.711

1.064

1.923

3.357

5

0.412

0.554

0.831

1.145

1.610

2.675

4.351

6

0.676

0.872

1.237

1.635

2.204

3.455

5.348

7

0.989

1.239

1.690

2.167

2.833

4.255

6.346

8

1.344

1.646

2.180

2.733

3.490

5.071

7.344

9

1.735

2.088

2.700

3.325

4.168

5.899

8.343

10

2.156

2.558

3.247

3.940

4.865

6.737

9.342

11

2.603

3.053

3.816

4.575

5.578

7.584

10.341

12

3.074

3.571

4.404

5.226

6.304

8.438

11.340

13

3.565

4.107

5.009

5.892

7.042

9.299

12.340

14

4.075

4.660

5.629

6.571

7.790

10.165

13.339

15

4.601

5.229

6.262

7.261

8.547

11.036

14.339

16

5.142

5.812

6.908

7.962

9.312

11.912

15.338

17

5.697

6.408

7.564

8.672

10.085

12.792

16.338

18

6.265

7.015

8.231

9.390

10.865

13.675

17.338

19

6.844

7.633

8.907

10.117

11.651

14.562

18.338

20

7.434

8.260

9.591

10.851

12.443

15.452

19.337

21

8.034

8.897

10.283

11.591

13.240

16.344

20.337

22

8.643

9.542

10.982

12.338

14.041

17.240

21.337

23

9.260

10.196

11.688

13.091

14.848

18.137

22.337

24

9.886

10.856

12.401

13.848

15.659

19.037

23.337

25

10.520

11.524

13.120

14.611

16.473

19.939

24.337

26

11.160

12.198

13.844

15.379

17.292

20.843

25.336

27

11.808

12.879

14.573

16.151

18.114

21.749

26.336

28

12.461

13.565

15.308

16.928

18.939

22.657

27.336

29

13.121

14.256

16.047

17.708

19.768

23.567

28.336

30

13.787

14.953

16.791

18.493

20.599

24.478

29.336

40

20.707

22.164

24.433

26.509

29.051

33.660

39.335

50

27.991

29.707

32.357

34.764

37.689

42.942

49.335

60

35.535

37.485

40.482

43.188

46.459

52.294

59.335

70

43.275

45.442

48.758

51.739

55.329

61.698

69.334

80

51.172

53.540

57.153

60.391

64.278

71.145

79.334

90

59.196

61.754

65.647

69.126

73.291

80.625

89.334

100

67.328

70.065

74.222

77.929

82.358

90.133

99.334

df

.250

.100

.050

.025

.010

.005

.001

1

1.323

2.706

3.841

5.024

6.635

7.879

10.828

2

2.773

4.605

5.991

7.378

9.210

10.597

13.816

3

4.108

6.251

7.815

9.348

11.345

12.838

16.266

4

5.385

7.779

9.488

11.143

13.277

14.860

18.467

5

6.626

9.236

11.070

12.832

15.086

16.750

20.515

6

7.841

10.645

12.592

14.449

16.812

18.548

22.458

7

9.037

12.017

14.067

16.013

18.475

20.278

24.322

8

10.219

13.362

15.507

17.535

20.090

21.955

26.125

9

11.389

14.684

16.919

19.023

21.666

23.589

27.871

10

12.549

15.987

18.307

20.483

23.209

25.188

29.588

11

13.701

17.275

19.675

21.920

24.725

26.757

31.264

12

14.845

18.549

21.026

23.337

26.217

28.300

32.909

13

15.984

19.812

22.362

24.736

27.688

29.819

34.528

14

17.117

21.064

23.685

26.119

29.141

31.319

36.123

15

18.245

22.307

24.996

27.488

30.578

32.801

37.697

16

19.369

23.542

26.296

28.845

32.000

34.267

39.252

17

20.489

24.769

27.587

30.191

33.409

35.718

40.790

18

21.605

25.989

28.869

31.526

34.805

37.156

43.312

19

22.718

27.204

30.144

32.852

36.191

38.582

43.820

20

23.828

28.412

31.410

34.170

37.566

39.997

45.315

21

24.935

29.615

32.671

35.479

38.932

41.401

46.797

22

26.039

30.813

33.924

36.781

40.289

42.796

48.268

23

27.141

32.007

35.172

38.076

41.638

44.181

49.728

24

28.241

33.196

36.415

39.364

42.980

45.558

51.179

25

29.339

34.382

37.652

40.646

44.314

46.928

52.620

26

30.434

35.563

38.885

41.923

45.642

48.290

54.052

27

31.528

36.741

40.113

43.194

46.963

49.645

55.476

28

32.620

37.916

41.337

44.461

48.278

50.993

56.892

29

33.711

39.087

42.557

45.722

49.588

52.336

58.302

30

34.800

40.256

43.773

46.979

50.892

53.672

59.703

40

45.616

51.805

55.758

59.342

63.691

66.766

73.402

50

56.334

63.167

67.505

71.420

76.154

79.490

86.661

60

66.981

74.397

79.082

83.298

88.379

91.952

99.607

70

77.577

85.527

90.531

95.0231

100.425

104.215

112.317

80

88.130

96.578

101.879

106.629

112.329

116.321

124.839

90

98.650

107.565

113.145

118.136

124.116

128.299

137.208

100

109.141

118.498

124.342

129.561

135.807

140.169

149.449

Table IV: F Distribution (tabulated values for a = .05)

D/N

1

2

3

4

5

6

7

8

9

10

1

161.40

199.50

215.70

224.60

230.20

234.00

236.80

238.90

240.50

241.90

2

18.51

19.00

19.16

19.25

19.30

19.33

19.35

19.37

19.38

19.40

3

10.13

9.55

9.28

9.12

9.01

8.94

8.89

8.85

8.81

8.79

4

7.71

6.94

6.59

6.39

6.26

6.16

6.09

6.04

6.00

5.96

5

6.61

5.79

5.41

5.19

5.05

4.95

4.88

4.82

4.77

4.74

6

5.99

5.14

4.76

4.53

4.39

4.28

4.21

4.15

4.10

4.06

7

5.59

4.74

4.35

4.12

3.97

3.87

3.79

3.73

3.68

3.64

8

5.32

4.46

4.07

3.84

3.69

3.58

3.50

3.44

3.39

3.35

9

5.12

4.26,

3.86

3.63

3.48

3.37

3.29

3.23

3.18

3.14

10

4.96

4.10

3.71

3.48

3.33

3.22

3.14

3.07

3.02

2.98

11

4.84

3.98

3.59

3.36

3.20

3.09

3.01

2.95

2.90

2.85

12

4.75

3.89

3.49

3.26

3.11

3.00

2.91

2.85

2.80

2.75

13

4.67

3.81

3.41

3.18

3.03

2.92

2.83

2.77

2.71

2.67

14

4.60

3.74

3.34

3.11

2.96

2.85

2.76

2.70

2.65

2.60

15

4.54

3.68

3.29

3.06

2.90

2.79

2.71

2.64

2.59

2.54

16

4.49

3.63

3.24

3.01

2.85

2.74

2.66

2.59

2.54

2.49

17

4.45

3.59

3.20

2.96

2.81

2.70

2.61

2.55

2.49

2.45

18

4.41

3.55

3.16

2.93

2.77

2.66

2.58

2.51

2.46

2.41

19

4.38

3.52

3.13

2.90

2.74

2.63

2.54

2.48

2.42

2.38

20

4.35

3.49

3.10

2.87

2.71

2.60

2.51

2.45

2.39

2.35

21

4.32

3.47

3.07

2.84

2.68

2.57

2.49

2.42

2.37

2.32

22

4.30

3.44

3.05

2.82

2.66

2.55

2.46

2.40

2.34

2.30

23

4.28

3.42

3.03

2.80

2.64

2.53

2.44

2.37

2.32

2.27

24

4.26

3.40

3.01

2.78

2.62

2.51

2.42

2.36

2.30

2.25

25

4.24

3.39

2.99

2.76

2.60

2.49

2.40

2.34

2.28

2.24

26

4.23

3.37

2.98

2.74

2.59

2.47

2.39

2.32

2.27

2.22

27

4.21

3.35

2.96

2.73

2.57

2.46

2.37

2.31

2.25

2.20

28

4.20

3.34

2.95

2.71

2.56

2.45

2.36

2.29

2.24

2.19

29

4.18

3.33

2.93

2.70

2.55

2.43

2.35

2.28

2.22

2.18

30

4.17

3.32

2.92

2.69

2.53

2.42

2.33

2.27

2.21

2.16

40

4.08

3.23

2.84

2.61

2.45

2.34

2.25

2.18

2.12

2.08

60

4.00

3.15

2.76

2.53

2.37

2.25

2.17

2.10

2.04

1.99

120

3.92

3.07

2.68

2.45

2.29

2.17

2.09

2.02

1.96

1.91

ˆ

3.84

3.00

2.60

2.37

2.21

2.10

2.01

1.94

1.88

1.83

D/N

12

15

20

24

30

40

60

120

00

1

243.90

245.90

248.00

249.10

250.10

251.10

252.20

253.30

254.30

2

19.41

19.43

19.45

19.45

19.46

19.47

19.48

19.49

19.50

3

8.74

8.70

8.66

8.64

8.62

8.59

8.57

8.55

8.53

4

5.91

5.86

5.80

5.77

5.75

5.72

5.69

5.66

5.63

5

4.68

4.62

4.56

4.53

4.50

4.46

4.43

4.40

4.36

6

4.00

3.94

3.87

3.84

3.81

3.77

3.74

3.70

3.67

7

3.57

3.51

3.44

3.41

3.38

3.34

3.30

3.27

3.23

8

3.28

3.22

3.15

3.12

3.08

3.04

3.01

2.97

2.93

9

3.07

3.01

2.94

2.90

2.86

2.83

2.79

2.75

2.71

10

2.91

2.85

2.77

2.74

2.70

2.66

2.62

2.58

2.54

11

2.79

2.72

2.65

2.61

2.57

2.53

2.49

2.45

2.40

12

2.69

2.62

2.54

2.51

2.47

2.43

2.38

2.34

2.30

13

2.60

2.53

2.46

2.42

2.38

2.34

2.30

2.25

2.21

14

2.53

2.46

2.39

2.35

2.31

2.27

2.22

2.18

2.13

15

2.48

2.40

2.33

2.29

2.25

2.20

2.16

2.11

2.07

16

2.42

2.35

2.28

2.24

2.19

2.15

2.11

2.06

2.01

17

2.38

2.31

2.23

2.19

2.15

2.10

2.06

2.01

1.96

18

2.34

2.27

2.19

2.15

2.11

2.06

2.02

1.97

1.92

19

2.31

2.23

2.16

2.11

2.07

2.03

1.98

1.93

1.88

20

2.28

2.20

2.12

2.08

2.04

1.99

1.95

1.90

1.84

21

2.25

2.18

2.10

2.05

2.01

1.96

1.92

1.87

1.81

22

2.23

2.15

2.07

2.03

1.98

1.94

1.89

1.84

1.78

23

2.20

2.13

2.05

2.01

1.96

1.91

1.86

1.81

1.76

24

2.18

2.11

2.03

1.98

1.94

1.89

1.84

1.79

1.73

25

2.16

2.09

2.01

1.96

1.92

1.87

1.82

1.77

1.71

26

2.15

2.07

1.99

1.95

1.90

1.85

1.80

1.75

1.69

27

2.13

2.06

1.97

1.93

1.88

1.84

1.79

1.73

1.67

28

2.12

2.04

1.96

1.91

1.87

1.82

1.77

1.71

1.65

29

2.10

2.03

1.94

1.90

1.85

1.81

1.75

1.70

1.64

30

2.09

2.01

1.93

1.89

1.84

1.79

1.74

1.68

1.62

40

2.00

1.92

1.84

1.79

1.74

1.69

1.64

1.58

1.51

60

1.92

1.84

1.75

1.70

1.65

1.59

1.53

1.47

1.39

120

1.83

1.75

1.66

1.61

1.55

1.50

1.43

1.35

1.25

ˆ

1.75

1.67

1.57

1.52

1.46

1.39

1.32

1.22

1.00

Table V: Exponential Distribution Values of for Various Values

Fractional parts of the total area (1.000) under the exponential curve are greater than X. To illustrate : if is 0.35, the probability of occurrence for a value greater than X is 0.7047.

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.0

1.000

0.9900

0.9802

0.9704

0.9608

0.9512

0.9418

0.9324

0.9231

0.9139

0.1

0.9048

0.8953

0.8860

0.8781

0.8694

0.8607

0.8521

0.8437

0.8353

0.8270

0.2

0.8187

0.8106

0.8025

0.7945

0.7866

0.7788

0.7711

0.7634

0.7558

0.7483

0.3

0.7408

0.7334

0.7261

0.7189

0.7118

0.7047

0.6977

0.6907

0.6839

0.6771

0.4

0.6703

0.6637

0.6570

0.6505

0.6440

0.6376

0.6313

0.6250

0.6188

0.6126

0.5

0.6065

0.6005

0.5945

0.5886

0.5827

0.5769

0.5713

0.5655

0.5599

0.5543

0.6

0.5488

0.5434

0.5379

0.5326

0.5273

0.5220

0.5169

0.5117

0.5066

0.5016

0.7

0.4966

0.4916

0.4868

0.4819

0.4771

0.4724

0.4677

0.4630

0.4584

0.4538

0.8

0.4493

0.4419

0.4404

0.4360

0.4317

0.4274

0.4232

0.4190

0.4148

0.4107

0.9

0.4066

0.4025

0.3985

0.3946

0.3906

0.3867

0.3820

0.3791

0.3753

0.3716

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.3679

0.3329

0.3012

0.2725

0.2466

0.2231

0.2019

0.1827

0.1653

0.1496

2.0

0.1353

0.1225

0.1108

0.1003

0.0907

0.0821

0.0743

0.0672

0.0608

0.0550

3.0

0.0498

0.0450

0.0408

0.0369

0.0334

0.0302

0.0273

0.0247

0.0224

0.0202

4.0

0.0183

0.0168

0.0150

0.0130

0.0123

0.0111

0.0101

0.0091

0.0082

0.0074

5.0

0.0067

0.0061

0.0055

0.0050

0.0045

0.0041

0.0037

0.0033

0.0030

0.0027

6.0

0.0025

0.0022

0.0020

0.0018

0.0017

0.0015

0.0014

0.0012

0.0011

0.0010

Based on the work of Selby, S.M., Ed. (1969). CRC Standard Mathematical Tables , 17th ed., CRC Press, Cleveland, OH, pp. 201“207.

Table VIa: 0.05 and 0.01 Points of the Distribution of ³ 1 Normal Universe (approximate values)

Probability that ³ 1 will exceed listed value in positive direction is

n

0.05

0.01

25

0.714

1.073

30

0.664

0.985

35

0.624

0.932

40

0.587

0.869

45

0.538

0.825

50

0.533

0.787

60

0.492

0.723

70

0.459

0.673

80

0.412

0.631

90

0.409

0.596

100

0.389

0.567

125

0.350

0.508

150

0.321

0.464

171

0.298

0.430

200

0.280

0.403

250

0.251

0.360

300

0.230

0.329

400

0.200

0.285

500

0.179

0.255

750

0.146

0.2108

1000

0.127

0.180

Note: For more information about this table see: Geary, R.C. and Pearson, E.S. (1938). Tests of Normality , Biometrica Office, London; D' Agostino, R.B. and Tietjem, G.L. (1973), Approaches to the null distribution of gamma 1, Biometrica , 60, pp. 169“173. The points listed are on the positive tail of the distribution. With a minus sign attached they are equally valid for the negative tail (D' Agnostine, R. and Pearson, E.S. (1973). Tests for departure from normality; empirical results for the distribution of gamma 1 and gamma 2, Biometrica , 68, pp. 613“622; Bowman, K.O. and Shenton, L.R. (1973). Notes on the distribution of gamma 1 in sampling from Pearson distributions, Biometrica , 60, pp. 155“167.

Table VIb: Percentage Points of the Distribution of ³ 2 : Normal Universe (approximate values)
 

Probability that ³ 2 Falls below ” Listed Value is

Probability that ³ 2 Falls above ” Listed Value is

n

0.01

0.03

0.05

0.01

23

-1.28

-1.09

1.16

2.30

30

-1.21

-1.02

1.11

2.21

40

-1.11

-0.93

1.06

2.04

30

-1.05

-0.85

0.99

1.88

73

-0.92

-0.73

0.87

1.59

100

-0.82

-0.65

0.77

1.39

123

-0.76

-0.60

0.71

1.24

130

-0.71

-0.55

0.65

1.13

200

-0.63

-0.49

0.57

0.98

250

-0.58

-0.45

0.52

0.87

300

-0.54

-0.41

0.47

0.79

300

-0.43

-0.33

0.37

0.60

1000

-0.32

-0.24

0.26

0.41

2000

-0.23

-0.17

0.18

0.28

3000

-0.15

-0.11

0.12

0.17

Note: For more information about this table see: Geary, R.C. and Pearson, E.S. (1938). Tests of Normality , Biometnca Office, London; Pearson, E.S. (1965). Tables of percentage points of gamma 1 and gamma 2 in normal samples, Biometnca , 52, pp. 282“285; D' Agnostmo, R.B. and Tietjem, G.L. (1971). Simulation probability points of gamma 2 for small samples, Biometrica , 58, pp. 669“672; D' Agnostine, R. and Pearson, E.S. (1973). Tests for departure from normality; empirical results for the distribution of gamma 1 and gamma 2, Biometrica , 68, pp. 613“622; Bowman, K.O. (1973). Power of the kurtosis statistic. Gamma 2 in tests of departure from normality, Biometrica , 60, pp. 623“628.

Table VII: A Guideline for Sample Size
 

± = 20%

± = 10%

a =5%

± = 1%

/ ƒ

20%

10%

5%

1%

20%

10%

5%

1%

20%

10%

5%

1%

20%

10%

5%

1%

 

0.2

225

328

428

651

309

428

541

789

392

525

650

919

584

744

891

1202

0.3

100

146

190

289

137

190

241

350

174

234

289

408

260

331

396

534

0.4

56

82

107

163

77

107

135

197

98

131

162

230

146

186

223

300

0.5

36

53

69

104

49

69

87

126

63

84

104

147

93

119

143

192

0.6

25

36

48

72

34

48

60

88

44

58

72

102

65

83

99

134

0.7

18

27

35

53

25

35

44

64

32

43

53

75

48

61

73

98

0.8

14

21

27

41

19

27

34

49

25

33

41

57

36

46

56

75

0.9

11

16

21

32

15

21

27

39

19

26

32

45

29

37

44

59

1.0

9

13

17

26

12

17

22

32

16

21

26

37

23

30

36

48

1.1

7

11

14

22

10

14

18

26

13

17

21

30

19

25

29

40

1.2

6

9

12

18

9

12

15

22

11

15

18

26

16

21

25

33

1.3

5

8

10

15

7

10

13

19

9

12

15

22

14

18

21

28

1.4

5

7

9

13

6

9

11

16

8

11

13

19

12

15

18

25

1.5

4

6

8

12

5

8

10

14

7

9

12

16

10

13

16

21

1.6

4

5

7

10

5

7

8

12

6

8

10

14

9

12

14

19

1.7

3

5

6

9

4

6

7

11

5

7

9

13

8

10

12

17

1.8

3

4

5

8

4

5

7

10

5

6

8

11

7

9

11

15

1.9

2

4

5

7

3

5

6

9

4

6

7

10

6

8

10

13

2.0

2

3

4

7

3

4

5

8

4

5

6

9

6

7

9

12

2.1

2

3

4

6

3

4

5

7

4

5

6

'8

5

7

8

11

2.2

2

3

4

5

3

4

4

7

3

4

5

8

5

6

7

10

2.3

2

2

3

5

2

3

4

6

3

4

5

7

4

6

7

9

2.4

2

2

3

5

2

3

4

5

3

4

5

6

4

5

6

8

2.5

1

2

3

4

2

3

3

5

3

3

4

6

4

5

6

8

2.6

1

2

3

4

2

3

3

5

2

3

4

5

3

4

5

7

2.7

1

2

2

4

2

2

3

4

2

3

4

5

3

4

5

7

2.8

1

2

2

3

2

2

3

4

2

3

3

5

3

4

5

6

2.9

1

2

2

3

1

2

3

4

2

2

3

4

3

4

4

6

3.0

1

1

2

3

1

2

2

4

2

2

3

4

3

3

4

5

3.1

1

1

2

3

1

2

2

3

2

2

3

4

2

3

4

5

3.2

1

1

2

3

1

2

2

3

2

2

3

4

2

3

3

5

3.3

1

1

2

2

1

2

2

3

1

2

2

3

2

3

3

4

3.4

1

1

1

2

1

1

2

3

1

2

2

3

2

3

3

4

3.5

1

1

1

2

1

1

2

3

1

2

2

3

2

2

3

4

3.6

1

1

1

2

1

1

2

2

1

2

2

3

2

2

3

4

3.7

1

1

1

2

1

1

2

2

1

2

2

3

2

2

3

4

3.8

1

1

1

2

1

1

1

2

1

1

2

3

2

2

2

3

3.9

1

1

1

2

1

1

1

2

1

1

2

2

2

2

2

3

4.0

1

1

1

2

1

1

1

2

1

1

2

2

1

2

2

3

Table VIII: Table for Testing Randomness of Grouping in a Sequence of Alternatives

s\r

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

6

3

                           

7

4

4

                         

8

4

4

5

                       

9

4

5

5

6

                     

10

5

5

6

6

6

                   

11

5

5

6

6

7

7

                 

12

5

6

6

7

7

8

8

               

13

5

6

6

7

8

8

9

9

             

14

5

6

7

7

8

8

9

9

10

           

15

6

6

7

8

8

9

9

10

10

11

         

16

6

6

7

8

8

9

10

10

11

11

11

       

17

6

7

7

8

9

9

10

10

11

11

12

12

     

18

6

7

8

8

9

10

10

11

11

12

12

13

13

   

19

6

7

8

8

9

10

10

11

12

12

13

13

14

14

 

20

6

7

8

9

9

10

11

11

12

12

13

13

14

14

15

Note: Probability of an equal or smaller number of runs than that listed is p = 0.05.

r = cases on the other side of average; r always taken as the smaller number of cases;

s = cases on one side of average; s the larger.

Source: Duncan, A.J. (1986). Quality Control and Industrial Statistics , 5th ed., Irwin, Homewood, IL.

Table IX: Conversion of Z-Score, DPMO, %Defective, and Yield

Z-Value

DPMO

% Defective

Yield

0.00

500000.0

50.0%

50.0%

0.01

496010.6

49.6%

50.4%

0.02

492021.6

49.2%

50.8%

0.03

488033.5

48.8%

51.2%

0.04

484046.5

48.4%

51.6%

0.05

480061.1

48.0%

52.0%

0.06

476077.7

47.6%

52.4%

0.07

472096.8

47.2%

52.8%

0.08

468118.6

46.8%

53.2%

0.09

464143.5

46.4%

53.6%

0.10

460172.1

46.0%

54.0%

0.11

456204.6

45.6%

54.4%

0.12

452241.5

45.2%

54.8%

0:13

448283.2

44.8%

55.2%

0.14

444330.0

44.4%

55.6%

0.15

440382.3

44.0%

56.0%

0.16

436440.5

43.6%

56.4%

0.17

432505.1

43.3%

56.7%

0.18

428576.3

42.9%

57.1%

0.19

424654.6

42.5%

57.5%

0.20

420740.3

42.1%

57.9%

0.21

416833.9

41.7%

58.3%

0.22

412935.6

41.3%

58.7%

0.23

409045.9

40.9%

59.1%

0.24

405165.2

40.5%

59.5%

0.25

401293.7

40.1%

59.9%

0.26

397431.9

39.7%

60.3%

0.27

393580.2

39.4%

60.6%

0.28

389738.8

39.0%

61.0%

0.29

385908.2

38.6%

61.4%

0.30

382088.6

38.2%

61.8%

0.31

378280.5

37.8%

62.2%

0.32

374484.2

37.4%

62.6%

0.33

370700.0

37.1%

62.9%

0.34

366928.3

36.7%

63.3%

0.35

363169.4

36.3%

63.7%

0.36

359423.6

35.9%

64.1%

0.37

355691.3

35.6%

64.4%

0.38

351972.8

35.2%

64.8%

0.39

348268.3

34.8%

65.2%

0.40

344578.3

34.5%

65.5%

0.41

340903.0

34.1%

65.9%

0.42

337242.8

33.7%

66.3%

0.43

333597.9

33.4%

66.6%

0.44

329968.6

33.0%

67.0%

0.45

326355.2

32.6%

67.4%

0.46

322758.1

32.3%

67.7%

0.47

319177.5

31.9%

68.1%

0.48

315613.7

31.6%

68.4%

0.49

312066.9

31.2%

68.8%

0.50

308537.5

30.9%

69.1%

0.51

305025.7

30.5%

69.5%

0.52

301531.8

30.2%

69.8%

0.53

298055.9

29.8%

70.2%

0.54

294598.5

29.5%

70.5%

0.55

291159.7

29.1%

70.9%

0.56

287739.7

28.8%

71.2%

0.57

284338.8

28.4%

71.6%

0.58

280957.3

28.1%

71.9%

0.59

277595.3

27.8%

72.2%

0.60

274253.1

27.4%

72.6%

0.61

270930.8

27.1%

72.9%

0.62

267628.8

26.8%

73.2%

0.63

264347.2

26.4%

73.6%

0.64

261086.2

26.1%

73.9%

0.65

257846.0

25.8%

74.2%

0.66

254626.8

25.5%

74.5%

0.67

251428.8

25.1%

74.9%

0.68

248252.2

24.8%

75.2%

0.69

245097.0

24.5%

75.5%

0.70

241963.6

24.2%

75.8%

0.71

238852.0

23.9%

76.1%

0.72

235762.4

23.6%

76.4%

0.73

232695.0

23.3%

76.7%

0.74

229649.9

23.0%

77.0%

0.75

226627.3

22.7%

77.3%

0.76

223627.2

22.4%

77.6%

0.77

220649.9

22.1%

77.9%

0.78

217695.4

21.8%

78.2%

0.79

214763.8

21.5%

78.5%

0.80

211855.3

21.2%

78.8%

0.81

208970.0

20.9%

79.1%

0.82

206108.0

20.6%

79.4%

0.83

203269.3

20.3%

79.7%

0.84

200454.1

20.0%

80.0%

0.85

197662.5

19.8%

80.2%

0.86

194894.5

19.5%

80.5%

0.87

192150.2

19.2%

80.8%

0.88

189429.6

18.9%

81.1%

0.89

186732.9

18.7%

81.3%

0.90

184060.1

18.4%

81.6%

0.91

181411.2

18.1%

81.9%

0.92

178786.4

17.9%

82.1%

0.93

176185.5

17.6%

82.4%

0.94

173608.8

17.4%

82.6%

0.95

171056.1

17.1%

82.9%

0.96

168527.6

16.9%

83.1%

0.97

166023.2

16.6%

83.4%

0.98

163543.1

16.4%

83.6%

0.99

161087.1

16.1%

83.9%

1.00

158655.3

15.9%

84.1%

1.01

156247.7

15.6%

84.4%

1.02

153864.2

15.4%

84.6%

1.03

151505.0

15.2%

84.8%

1.04

149170.0

14.9%

85.1%

1.05

146859.1

14.7%

85.3%

1.06

144572.3

14.5%

85.5%

1.07

142309.7

14.2%

85.8%

1.08

140071.1

14.0%

86.0%

1.09

137856.6

13.8%

86.2%

1.10

135666.1

13.6%

86.4%

1.11

133499.6

13.3%

86.7%

1.12

131356.9

13.1%

86.9%

1.13

129238.2

12.9%

87.1%

1.14

127143.2

12.7%

87.3%

1.15

125072.0

12.5%

87.5%

1.16

123024.5

12.3%

87.7%

1.17

121000.5

12.1%

87.9%

1.18

119000.2

11.9%

88.1%

1.19

117023.3

11.7%

88.3%

1.20

115069.7

11.5%

88.5%

1.21

113139.5

11.3%

88.7%

1.22

111232.5

11.1%

88.9%

1.23

109348.6

10.9%

89.1%

1.24

107487.8

10.7%

89.3%

1.25

105649.8

10.6%

89.4%

1.26

103834.7

10.4%

89.6%

1.27

102042.4

10.2%

89.8%

1.28

100272.6

10.0%

90.0%

1.29

98525.4

9.9%

90.1%

1.30

96800.5

9.7%

90.3%

1.31

95098.0

9.5%

90.5%

1.32

93417.6

9.3%

90.7%

1.33

91759.2

9.2%

90.8%

1.34

90122.7

9.0%

91.0%

1.35

88508.1

8.9%

91.1%

1.36

86915.0

8.7%

91.3%

1.37

85343.5

8.5%

91.5%

1.38

83793.4

8.4%

91.6%

1.39

82264.5

8.2%

91.8%

1.40

80756.7

8.1%

91.9%

1.41

79269.9

7.9%

92.1%

1.42

77803.9

7.8%

92.2%

1.43

76358.6

7.6%

92.4%

1.44

74933.7

7.5%

92.5%

1.45

73529.3

7.4%

92.6%

1.46

72145.1

7.2%

92.8%

1.47

70780.9

7.1%

92.9%

1.48

69436.7

6.9%

93.1%

1.49

68112.1

6.8%

93.2%

1.50

66807.2

6.7%

93.3%

1.51

65521.7

6.6%

93.4%

1.52

64255.5

6.4%

93.6%

1.53

63008.4

6.3%

93.7%

1.54

61780.2

6.2%

93.8%

1.55

60570.8

6.1%

93.9%

1.56

59380.0

5.9%

94.1%

1.57

58207.6

5.8%

94.2%

1.58

57053.4

5.7%

94.3%

1.59

55917.4

5.6%

94.4%

1.60

54799.3

5.5%

94.5%

1.61

53698.9

5.4%

94.6%

1.62

52616.1

5.3%

94.7%

1.63

51550.7

5.2%

94.8%

1.64

50502.6

5.1%

94.9%

1.65

49471.5

4.9%

95.1%

1.66

48457.2

4.8%

95.2%

1.67

47459.7

4.7%

95.3%

1.68

46478.6

4.6%

95.4%

1.69

45513.9

4.6%

95.4%

1.70

44565.4

4.5%

95.5%

1.71

43632.9

4.4%

95.6%

1.72

42716.2

4.3%

95.7%

1.73

41815.1

4.2%

95.8%

1.74

40929.5

4.1%

95.9%

1.75

40059.1

4.0%

96.0%

1.76

39203.9

3.9%

96.1%

1.77

38363.5

3.8%

96.2%

1.78

37537.9

3.8%

96.2%

1.79

36726.9

3.7%

96.3%

1.80

35930.3

3.6%

96.4%

1.81

35147.8

3.5%

96.5%

1.82

34379.4

3.4%

96.6%

1.83

33624.9

3.4%

96.6%

1.84

32884.1

3.3%

96.7%

1.85

32156.7

3.2%

96.8%

1.86

31442.7

3.1%

96.9%

1.87

30741.8

3.1%

96.9%

1.88

30054.0

3.0%

97.0%

1.89

29378.9

2.9%

97.1%

1.90

28716.5

2.9%

97.1%

1.91

28066.5

2.8%

97.2%

1.92

27428.9

2.7%

97.3%

1.93

26803.3

2.7%

97.3%

1.94

26189.8

2.6%

97.4%

1.95

25588.0

2.6%

97.4%

1.96

24997.8

2.5%

97.5%

1.97

24419.1

2.4%

97.6%

1.98

23851.7

2.4%

97.6%

1.99

23295.4

2.3%

97.7%

2.00

22750.1

2.3%

97.7%

2.01

22215.5

2.22%

97.78%

2.02

21691.6

2.17%

97.83%

2.03

21178.2

2.12%

97.88%

2.04

20675.1

2.07%

97.93%

2.05

20182.1

2.02%

97.98%

2.06

19699.2

1.97%

98.03%

2.07

19226.1

1.92%

98.08%

2.08

18762.7

1.88%

98.12%

2.09

18308.8

1.83%

98.17%

2.10

17864.4

1.79%

98.21%

2.11

17429.1

1.74%

98.26%

2.12

17003.0

1.70%

98.30%

2.13

16585.7

1.66%

98.34%

2.14

16177.3

1.62%

98.38%

2.15

15777.6

1.58%

98.42%

2.16

15386.3

1.54%

98.46%

2.17

15003.4

1.50%

98.50%

2.18

14628.7

1.46%

98.54%

2.19

14262.1

1.43%

98.57%

2.20

13903.4

1.39%

98.61%

2.21

13552.5

1.36%

98.64%

2.22

13209.3

1.32%

98.68%

2.23

12873.7

1.29%

98.71%

2.24

12545.4

1.25%

98.75%

2.25

12224.4

1.22%

98.78%

2.26

11910.6

1.19%

98.81%

2.27

11603.8

1.16%

98.84%

2.28

11303.8

1.13%

98.87%

2.29

11010.6

1.10%

98.90%

2.30

10724.1

1.07%

98.93%

2.31

10444.1

1.04%

98.96%

2.32

10170.4

1.02%

98.98%

2.33

9903.1

0.99%

99.01%

2.34

9641.8

0.96%

99.04%

2.35

9386.7

0.94%

99.06%

2.36

9137.5

0.91%

99.09%

2.37

8894.0

0.89%

99.11%

2.38

8656.3

0.87%

99.13%

2.39

8424.2

0.84%

99.16%

2.40

8197.5

0.82%

99.18%

2.41

7976.3

0.80%

99.20%

2.42

7760.3

0.78%

99.22%

2.43

7549.4

0.75%

99.25%

2.44

7343.6

0.73%

99.27%

2.45

7142.8

0.71%

99.29%

2.46

6946.9

0.69%

99.31%

2.47

6755.7

0.68%

99.32%

2.48

6569.1

0.66%

99.34%

2.49

6387.2

0.64%

99.36%

2.50

6209.7

0.62%

99.38%

2.51

6036.6

0.60%

99.40%

2.52

5867.8

0.59%

99.41%

2.53

5703.1

0.57%

99.43%

2.54

5542.6

0.55%

99.45%

2.55

5386.2

0.54%

99.46%

2.56

5233.6

0.52%

99.48%

2.57

5085.0

0.51%

99.49%

2.58

4940.0

0.49%

99.51%

2.59

4798.8

0.48%

99.52%

2.60

4661.2

0.47%

99.53%

2.61

4527.1

0.45%

99.55%

2.62

4396.5

0.44%

99.56%

2.63

4269.3

0.43%

99.57%

2.64

4145.3

0.41%

99.59%

2.65

4024.6

0.40%

99.60%

2.66

3907.1

0.39%

99.61%

2.67

3792.6

0.38%

99.62%

2.68

3681.2

0.37%

99.63%

2.69

3572.6

0.36%

99.64%

2.70

3467.0

0.35%

99.65%

2.71

3364.2

0.34%

99.66%

2.72

3264.1

0.33%

99.67%

2.73

3166.8

0.32%

99.68%

2.74

3072.0

0.31%

99.69%

2.75

2979.8

0.30%

99.70%

2.76

2890.1

0.29%

99.71%

2.77

2802.9

0.28%

99.72%

2.78

2718.0

0.27%

99.73%

2.79

2635.5

0.26%

99.74%

2.80

2555.2

0.26%

99.74%

2.81

2477.1

0.25%

99.75%

2.82

2401.2

0.24%

99.76%

2.83

2327.5

0.23%

99.77%

2.84

2255.7

0.23%

99.77%

2.85

2186.0

0.22%

99.78%

2.86

2118.3

0.21%

99.79%

2.87

2052.4

0.21%

99.79%

2.88

1988.4

0.20%

99.80%

2.89

1926.3

0.19%

99.81%

2.90

1865.9

0.19%

99.81%

2.91

1807.2

0.18%

99.82%

2.92

1750.2

0.18%

99.82%

2.93

1694.9

0.17%

99.83%

2.94

1641.1

0.16%

99.84%

2.95

1588.9

0.16%

99.84%

2.96

1538.3

0.15%

99.85%

2.97

1489.1

0.15%

99.85%

2.98

1441.3

0.14%

99.86%

2.99

1395.0

0.14%

99.86%

3.00

1350.0

0.13%

99.87%

3.01

1306.3

0.131%

99.869%

3.02

1263.9

0.126%

99.874%

3.03

1222.8

0.122%

99.878%

3.04

1183.0

0.118%

99.882%

3.05

1144.3

0.114%

99.886%

3.06

1106.8

0.111%

99.889%

3.07

1070.4

0.107%

99.893%

3.08

1035.1

0.104%

99.896%

3.09

1000.9

0.100%

99.900%

3.10

967.7

0.097%

99.903%

3.11

935.5

0.094%

99.906%

3.12

904.3

0.090%

99.910%

3.13

874.1

0.087%

99.913%

3.14

844.8

0.084%

99.916%

3.15

816.4

0.082%

99.918%

3.16

788.9

0.079%

99.921%

3.17

762.3

0.076%

99.924%

3.18

736.4

0.074%

99.926%

3.19

711.4

0.071%

99.929%

3.20

687.2

0.069%

99.931%

3.21

663.7

0.066%

99.934%

3.22

641.0

0.064%

99.936%

3.23

619.0

0.062%

99.938%

3.24

597.7

0.060%

99.940%

3.25

577.1

0.058%

99.942%

3.26

557.1

0.056%

99.944%

3.27

537.8

0.054%

99.946%

3.28

519.1

0.052%

99.948%

3.29

501.0

0.050%

99.950%

3.30

483.5

0.048%

99.952%

3.31

466.5

0.047%

99.953%

3.32

450.1

0.045%

99.955%

3.33

434.3

0.043%

99.957%

3.34

418.9

0.042%

99.958%

3.35

404.1

0.040%

99.960%

3.36

389.8

0.039%

99.961%

3.37

375.9

0.038%

99.962%

3.38

362.5

0.036%

99.964%

3.39

349.5

0.035%

99.965%

3.40

337.0

0.034%

99.966%

3.41

324.9

0.032%

99.968%

3.42

313.2

0.031%

99.969%

3.43

301.8

0.030%

99.970%

3.44

290.9

0.029%

99.971%

3.45

280.3

0.028%

99.972%

3.46

270.1

0.027%

99.973%

3.47

260.3

0.026%

99.974%

3.48

250.8

0.025%

99.975%

3.49

241.6

0.024%

99.976%

3.50

232.7

0.023%

99.977%

3.51

224.1

0.022%

99.978%

3.52

215.8

0.022%

99.978%

3.53

207.8

0.021%

99.979%

3.54

200.1

0.020%

99.980%

3.55

192.7

0.019%

99.981%

3.56

185.5

0.019%

99.981%

3.57

178.5

0.018%

99.982%

3.58

171.8

0.017%

99.983%

3.59

165.4

0.017%

99.983%

3.60

159.1

0.016%

99.984%

3.61

153.1

0.015%

99.985%

3.62

147.3

0.015%

99.985%

3.63

141.7

0.014%

99.986%

3.64

136.4

0.014%

99.986%

3.65

131.2

0.013%

99.987%

3.66

126.1

0.013%

99.987%

3.67

121.3

0.012%

99.988%

3.68

116.6

0.012%

99.988%

3.69

112.2

0.011%

99.989%

3.70

107.8

0.011%

99.989%

3.71

103.7

0.010%

99.990%

3.72

99.6

0.010%

99.990%

3.73

95.8

0.010%

99.990%

3.74

92.0

0.009%

99.991%

3.75

88.4

0.009%

99.991%

3.76

85.0

0.008%

99.992%

3.77

81.6

0.008%

99.992%

3.78

78.4

0.008%

99.992%

3.79

75.3

0.008%

99.992%

3.80

72.4

0.007%

99.993%

3.81

69.5

0.007%

99.993%

3.82

66.7

0.007%

99.993%

3.83

64.1

0.006%

99.994%

3.84

61.5

0.006%

99.994%

3.85

59.1

0.006%

99.994%

3.86

56.7

0.006%

99.994%

3.87

54.4

0.005%

99.995%

3.88

52.2

0.005%

99.995%

3.89

50.1

0.005%

99.995%

3.90

48.1

0.005%

99.995%

3.91

46.2

0.005%

99.995%

3.92

44.3

0.004%

99.996%

3.93

42.5

0.004%

99.996%

3.94

40.8

0.004%

99.996%

3.95

39.1

0.004%

99.996%

3.96

37.5

0.004%

99.996%

3.97

36.0

0.004%

99.996%

3.98

34.5

0.003%

99.997%

3.99

33.1

0.003%

99.997%

4.00

31.7

0.003%

99.997%

4.01

30.4

0.0030%

99.9970%

4.02

29.1

0.0029%

99.9971%

4.03

27.9

0.0028%

99.9972%

4.04

26.7

0.0027%

99.9973%

4.05

25.6

0.0026%

99.9974%

4.06

24.5

0.0025%

99.9975%

4.07

23.5

0.0024%

99.9976%

4.08

22.5

0.0023%

99.9977%

4.09

21.6

0.0022%

99.9978%

4.10

20.7

0.0021%

99.9979%

4.11

19.8

0.0020%

99.9980%

4.12

19.0

0.0019%

99.9981%

4.13

18.1

0.0018%

99.9982%

4.14

17.4

0.0017%

99.9983%

4.15

16.6

0.0017%

99.9983%

4.16

15.9

0.0016%

99.9984%

4.17

15.2

0.0015%

99.9985%

4.18

14.6

0.0015%

99.9985%

4.19

14.0

0.0014%

99.9986%

4.20

13.4

0.0013%

99.9987%

4.21

12.8

0.0013%

99.9987%

4.22

12.2

0.0012%

99.9988%

4.23

11.7

0.0012%

99.9988%

4.24

11.2

0.0011%

99.9989%

4.25

10.7

0.0011%

99.9989%

4.26

10.2

0.0010%

99.9990%

4.27

9.8

0.0010%

99.9990%

4.28

9.4

0.0009%

99.9991%

4.29

8.9

0.0009%

99.9991%

4.30

8.5

0.0009%

99.9991%

4.31

8.2

0.0008%

99.9992%

4.32

7.8

0.0008%

99.9992%

4.33

7.5

0.0007%

99.9993%

4.34

7.1

0.0007%

99.9993%

4.35

6.8

0.0007%

99.9993%

4.36

6.5

0.0007%

99.9993%

4.37

6.2

0.0006%

99.9994%

4.38

5.9

0.0006%

99.9994%

4.39

5.7

0.0006%

99.9994%

4.40

5.4

0.0005%

99.9995%

4.41

5.2

0.0005%

99.9995%

4.42

4.9

0.0005%

99.9995%

4.43

4.7

0.0005%

99.9995%

4.44

4.5

0.0005%

99.9995%

4.45

4.3

0.0004%

99.9996%

4.46

4.1

0.0004%

99.9996%

4.47

3.9

0.0004%

99.9996%

4.48

3.7

0.0004%

99.9996%

4.49

3.6

0.0004%

99.9996%

4.50

3.4

0.0003%

99.9997%

4.51

3.2

0.0003%

99.9997%

4.52

3.1

0.0003%

99.9997%

4.53

3.0

0.0003%

99.9997%

4.54

2.8

0.0003%

99.9997%

4.55

2.7

0.0003%

99.9997%

4.56

2.6

0.0003%

99.9997%

4.57

2.4

0.0002%

99.9998%

4.58

2.3

0.0002%

99.9998%

4.59

2.2

0.0002%

99.9998%

4.60

2.1

0.0002%

99.9998%

4.61

2.0

0.0002%

99.9998%

4.62

1.9

0.0002%

99.9998%

4.63

1.8

0.0002%

99.9998%

4.64

1.7

0.0002%

99.9998%

4.65

1.7

0.0002%

99.9998%

4.66

1.6

0.0002%

99.9998%

4.67

1.5

0.0002%

99.9998%

4.68

1.4

0.0001%

99.9999%

4.69

1.4

0.0001%

99.9999%

4.70

1.3

0.0001%

99.9999%

4.71

1.2

0.0001%

99.9999%

4.72

1.2

0.0001%

99.9999%

4.73

1.1

0.0001%

99.9999%

4.74

1.1

0.0001%

99.9999%

4.75

1.0

0.0001%

99.9999%

4.76

1.0

0.0001%

99.9999%

4.77

0.9

0.0001%

99.9999%

4.78

0.9

0.0001%

99.9999%

4.79

0.8

0.0001%

99.9999%

4.80

0.8

0.0001%

99.9999%

4.81

0.8

0.0001%

99.9999%

4.82

0.7

0.0001%

99.9999%

4.83

0.7

0.0001%

99.9999%

4.84

0.7

0.0001%

99.9999%

4.85

0.6

0.0001%

99.9999%

4.86

0.6

0.0001%

99.9999%

4.87

0.6

0.0001%

99.9999%

4.88

0.5

0.0001%

99.9999%

4.89

0.5

0.0001%

99.9999%

4.90

0.5

0.0000%

100.0000%

4.91

0.5

0.0000%

100.0000%

4.92

0.4

0.0000%

100.0000%

4.93

0.4

0.0000%

100.0000%

4.94

0.4

0.0000%

100.0000%

4.95

0.4

0.0000%

100.0000%

4.96

0.4

0.0000%

100.0000%

4.97

0.3

0.0000%

100.0000%

4.98

0.3

0.0000%

100.0000%

4.99

0.3

0.0000%

100.0000%

5.00

0.3

0.0000%

100.0000%

5.01

0.273

0.000027%

99.999973%

5.02

0.259

0.000026%

99.999974%

5.03

0.246

0.000025%

99.999975%

5.04

0.233

0.000023%

99.999977%

5.05

0.221

0.000022%

99.999978%

5.06

0.210

0.000021%

99.999979%

5.07

0.199

0.000020%

99.999980%

5.08

0.189

0.000019%

99.999981%

5.09

0.179

0.000018%

99.999982%

5.10

0.170

0.000017%

99.999983%

5.11

0.161

0.000016%

99.999984%

5.12

0.153

0.000015%

99.999985%

5.13

0.145

0.000015%

99.999985%

5.14

0.138

0.000014%

99.999986%

5.15

0.130

0.000013%

99.999987%

5.16

0.124

0.000012%

99.999988%

5.17

0.117

0.000012%

99.999988%

5.18

0.111

0.000011%

99.999989%

5.19

0.105

0.000011%

99.999989%

5.20

0.100

0.000010%

99.999990%

5.21

0.095

0.000009%

99.999991%

5.22

0.090

0.000009%

99.999991%

5.23

0.085

0.000008%

99.999992%

5.24

0.080

0.000008%

99.999992%

5.25

0.076

0.000008%

99.999992%

5.26

0.072

0.000007%

99.999993%

5.27

0.068

0.000007%

99.999993%

5.28

0.065

0.000006%

99.999994%

5.29

0.061

0.000006%

99.999994%

5.30

0.058

0.000006%

99.999994%

5.31

0.055

0.000005%

99.999995%

5.32

0.052

0.000005%

99.999995%

5.33

0.049

0.000005%

99.999995%

5.34

0.047

0.000005%

99.999995%

5.35

0.044

0.000004%

99.999996%

5.36

0.042

0.000004%

99.999996%

5.37

0.039

0.000004%

99.999996%

5.38

0.037

0.000004%

99.999996%

5.39

0.035

0.000004%

99.999996%

5.40

0.033

0.000003%

99.999997%

5.41

0.032

0.000003%

99.999997%

5.42

0.030

0.000003%

99.999997%

5.43

0.028

0.000003%

99.999997%

5.44

0.027

0.000003%

99.999997%

5.45

0.025

0.000003%

99.999997%

5.46

0.024

0.000002%

99.999998%

5.47

0.023

0:000002%

99.999998%

5.48

0.021

0.000002%

99.999998%

5.49

0.020

0.000002%

99.999998%

5.50

0.019

0.000002%

99.999998%

5.51

0.018

0.000002%

99.999998%

5.52

0.017

0.000002%

99.999998%

5.53

0.016

0.000002%

99.999998%

5.54

0.015

0.000002%

99.999998%

5.55

0.014

0.000001%

99.999999%

5.56

0.014

0.000001%

99.999999%

5.57

0.013

0.000001%

99.999999%

5.58

0.012

0.000001%

99.999999%

5.59

0.011

0.000001%

99.999999%

5.60

0.011

0.000001%

99.999999%

5.61

0.010

0.000001%

99.999999%

5.62

0.010

0.000001%

99.999999%

5.63

0.009

0.000001%

99.999999%

5.64

0.009

0.000001%

99.999999%

5.65

0.008

0.000001%

99.999999%

5.66

0.008

0.000001%

99.999999%

5.67

0.007

0.000001%

99.999999%

5.68

0.007

0.000001%

99.999999%

5.69

0.006

0.000001%

99.999999%

5.70

0.006

0.000001%

99.999999%

5.71

0.006

0.000001%

99.999999%

5.72

0.005

0.000001%

99.999999%

5.73

0.005

0.000001%

99.999999%

5.74

0.005

0.000000%

100.000000%

5.75

0.004

0.000000%

100.000000%

5.76

0.004

0.000000%

100.000000%

5.77

0.004

0.000000%

100.000000%

5.78

0.004

0.000000%

100.000000%

5.79

0.004

0.000000%

100.000000%

5.80

0.003

0.000000%

100.000000%

5.81

0.003

0.000000%

100.000000%

5.82

0.003

0.000000%

100.000000%

5.83

0.003

0.000000%

100.000000%

5.84

0.003

0.000000%

100.000000%

5.85

0.002

0.000000%

100.000000%

5.86

0.002

0.000000%

100.000000%

5.87

0.002

0.000000%

100.000000%

5.88

0.002

0.000000%

100.000000%

5.89

0.002

0.000000%

100.000000%

5.90

0.002

0.000000%

100.000000%

5.91

0.002

0.000000%

100.000000%

5.92

0.002

0.000000%

100.000000%

5.93

0.002

0.000000%

100.000000%

5.94

0.001

0.000000%

100.000000%

5.95

0.001

0.000000%

100.000000%

5.96

0.001

0.000000%

100.000000%

5.97

0.001

0.000000%

100.000000%

5.98

0.001

0.000000%

100.000000%

5.99

0.001

0.000000%

100.000000%

6.00

0.001

0.000000%

100.000000%




Six Sigma and Beyond. Statistical Process Control (Vol. 4)
Six Sigma and Beyond: Statistical Process Control, Volume IV
ISBN: 1574443135
EAN: 2147483647
Year: 2003
Pages: 181
Authors: D.H. Stamatis

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