Tablas

APPENDICES
APPENDIX A.
Table I Table II Table III Table IV Table V Chart VI Table VII Table VIII Table IX Table X Table XI

STATISTICAL TABLES AND CHARTS

651

Summary of Common Probability Distributions 652 Cumulative Standard Normal Distribution 653 Percentage Points 2 , of the Chi-Squared Distribution 655 Percentage Points t , of the t-Distribution 656 Percentage Points f , 1, 2 of theF-Distribution 657 Operating Characteristic Curves 662 Critical Values for the Sign Test 671 Critical Values for the Wilcoxon Signed-Rank Test 671 Critical Values for the Wilcoxon Rank-Sum Test 672 Factors for Constructing Variables Control Charts 673 Factors for Tolerance Intervals 674

APPENDIX B. APPENDIX C.

BIBLIOGRAPHY

677 679

ANSWERS TO SELECTED EXERCISES

649

Appendix AStatistical Tables and Charts

651

652

APPENDIX A

STATISTICAL TABLES AND CHARTS

Table I Summary of Common Probability Distributions Name Discrete Uniform Binomial x Geometric x Negative binomial x a r, r x r 1 n, a n a b px 11 x b p2 n
x

Probability Distribution

Mean 1b , 1 1 p 1 r p 1 a2 2 np 1b

Variance a 12 np11 p2 12 2 1

Section in Book

3-5 3-6

0, 1, . . . , n,0 11 p2 x 1p, 1, 2, . . . , 0 p

p

11 r11

p2 p2

3-7.1

1 b 11 p2 x rpr 1 1, r 2, . . . , 0 p K N K b a ba n x x N a b n

p2 p2

3-7.2

Hypergeometric

np, where p N K N

np11

p2 a

N N

n b 1

3-8

x e

max10, n min1K, n2, K
x

N

K2, 1, . . . N, n

Poisson Continuous Uniform

x!

,x

0, 1, 2, . . . , 0 1b 1b

3-9

b

Normal x ExponentialErlang Gamma Weibull x 22 0 1 x 1r
r r 1

12 1

1

a

,a e
1

x
21
x

b 22 ,0

a2 2

a2 2 12
2

4-5

4-6

, e x, 0 e x ,0 12!
x

x, 0 x, r x, 0
1

1 1, 2, . . . r, 0 r r a1 1 b
2 2

1 r r a1 a1
2

2 2

4-8 4-9.1 4-9.2 2 b bd
2

xr

e 1r2

1

,0 x a b x, 0 exp a

2

e

1x 2

,

4-10

,0 3 ln1x2 2 42 b e
2

c

1

Lognormal

2

2e2

1e

2

12

4-11

1z2

z

P1Z

z2

22 1

APPENDIX A

653

e

1 u2 2 du

Φ (z)

z

0

Table II Cumulative Standard Normal Distribution
z 3.9 3.8 3.7 3.6 3.5 3.4 3.3 3.2 3.1 3.0 2.9 2.8 2.7 2.6 2.5 2.4 2.3 2.2 2.1 2.0 1.9 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.09 0.000033 0.000050 0.000075 0.000112 0.000165 0.0002420.000350 0.000501 0.000711 0.001001 0.001395 0.001926 0.002635 0.003573 0.004799 0.006387 0.008424 0.011011 0.014262 0.018309 0.023295 0.029379 0.036727 0.045514 0.055917 0.068112 0.082264 0.098525 0.117023 0.137857 0.161087 0.186733 0.214764 0.245097 0.277595 0.312067 0.348268 0.385908 0.424655 0.464144 0.08 0.000034 0.000052 0.000078 0.000117 0.000172 0.000251 0.000362 0.000519 0.000736 0.0010350.001441 0.001988 0.002718 0.003681 0.004940 0.006569 0.008656 0.011304 0.014629 0.018763 0.023852 0.030054 0.037538 0.046479 0.057053 0.069437 0.083793 0.100273 0.119000 0.140071 0.163543 0.189430 0.217695 0.248252 0.280957 0.315614 0.351973 0.389739 0.428576 0.468119 0.07 0.000036 0.000054 0.000082 0.000121 0.000179 0.000260 0.000376 0.000538 0.000762 0.001070 0.001489 0.002052 0.002803 0.0037930.005085 0.006756 0.008894 0.011604 0.015003 0.019226 0.024419 0.030742 0.038364 0.047460 0.058208 0.070781 0.085343 0.102042 0.121001 0.142310 0.166023 0.192150 0.220650 0.251429 0.284339 0.319178 0.355691 0.393580 0.432505 0.472097 0.06 0.000037 0.000057 0.000085 0.000126 0.000185 0.000270 0.000390 0.000557 0.000789 0.001107 0.001538 0.002118 0.002890 0.003907 0.005234 0.006947 0.009137 0.0119110.015386 0.019699 0.024998 0.031443 0.039204 0.048457 0.059380 0.072145 0.086915 0.103835 0.123024 0.144572 0.168528 0.194894 0.223627 0.254627 0.287740 0.322758 0.359424 0.397432 0.436441 0.476078 0.05 0.000039 0.000059 0.000088 0.000131 0.000193 0.000280 0.000404 0.000577 0.000816 0.001144 0.001589 0.002186 0.002980 0.004025 0.005386 0.007143 0.009387 0.012224 0.015778 0.020182 0.025588...