Applied Statistics and Probability for Engineers

680 APPENDIX C ANSWERS TO SELECTED EXERCISES

2-65. (a) 4 499 0.0080

(b) (5500)(4499)0.000080

(c) (495500)(494499)0.98

2-67. (a) 0.813 (b) 0.632

(c) 0.764

Section 2-5

2-71. 0.22

2-73. 0.023

2-75. 0.028

2-77. (a) 0.0225 (b) 0.125

2-79. (a) 0.20 (b) 0.20

Section 2-6

2-81. No

2-83. No

2-85. (a) No (b) 0.733

2-87. (a) 0.59 (b) 0.328 (c) 0.41

2-89. (a) 0.00003 (b) 0.00024

(c) 0.00107

2-91. 0.9702

2-93. (a) No (b) Yes

Section 2-7

2-95. 0.003

2-97. (a) 0.615 (b) 0.618

(c) 0.052

2-99. (a) 0.9847 (b) 0.1184

Supplemental

2-101.The sample space S{A,A D 1 ,

A D 2 , A D 3 , A D 4 , A D 5 }

2-103.(a) 0.19 (b) 0.15 (c) 0.99

(d) 0.80 (e) 0.158

2-105.(a) No (b) No (c) 40 240

(d) 200240 (e) 234 400

(f ) 1

2-107.(a) 0.282 (b) 0.718

2-109.0.996

2-111.(a) 0.0037 (b) 0.811

2-113.(a) 0.0778 (b) 0.00108

(c) 0.947

2-115.(a) 0.9764 (b) 0.680

2-117.(a) 0.207 (b) 0.625 (c) 0.6

2-119.(a) 0.453 (b) 0.261

(c) 0.881 (d) 0.547

(e) 0.783 (f) 0.687

2-121.1.58  10 ^7

CHAPTER 3

Section 3-1

3-1. {0, 1, 2,..., 1000}

3-3. {0, 1, 2,..., 99999}

Section 3-2

3-13. fX(0) 1 3, fX(1.5) 1 3,

fX(2) 1 6, fX(3) 1  6

3-15. (a) 1 (b) 78 (c)^3  4

(d)^1  2

3-17. (a) 925 (b) 4 25

(c) 1225 (d) 1

3-19. P(X10 million)0.3,

P(X5 million)0.6,

P(X1 million)0.1

3-21. P(X0) 8  10 ^6 ,

P(X1)0.0012,

P(X2)0.0576,

P(X3)0.9412

3-23. P(X15 million)0.6,

P(X5 million)0.3,

P(X0.5 million)0.1

3-25. P(X0)0.00001,

P(X1)0.00167,

P(X2)0.07663,

P(X3)0.92169

Section 3-3

3-27. (a) 78 (b) 1 (c)^3  4

(d) 3 8

3-29. F(x)0 for x1 million; 0.1

for 1 million x5 million;

0.7 for 5 million x10 mil-

lion; 1 for 10 million x

3-31. F(x)0 for x0; 0.008 for

0 x1; 0.104 for 1 x2;

0.488 for 2 x 3; 1 for 3 x

3-33. (a) 1 (b) 0.5 (c) 0.5

(d) 0.5

3-35. (a) 1 (b) 0.75 (c) 0.25

(d) 0.25 (e) 0 (f ) 0

Section 3-4

3-37. E(X)2, V(X) 2

3-39. E(X)0, V(X)1.5

3-41. E(X)6.1 million,

V(X)7.89 million^2

3-43. E(X)2.4, V(X)0.48

3-45. x 24

Section 3-5

3-47. E(X)2, V(X)0.667

3-49. E(X)0.17, V(X)0.0002

3-51. E(X)590.45, V(X)0.0825

Section 3-6

3-57. (a) 0.2461 (b) 0.0547

(c) 0.0107 (d) 0.3223

3-59. (a) 2.4  10 ^8 (b) 0.99989

(c) 9.91  10 ^18

(d) 1.138  10 ^4

3-61. F(x)0 for x0; 0.4219 for

0 x1; 0.8438 for 1 x2;

0.9844 for 2 x3; 1 for 3 x

3-63. (a) 0.3681 (b) 0.6323

(c) 0.9198 (d)E(X)1,

V(X)0.999

3-65. (a)n50, p0.1

(b) 0.1117 (c) 4.51  10 ^48

3-67. (a) 0.9961 (b) 0.9886

3-69. (a) 0 (b) 0.2137

Section 3-7

3-71. (a) 0.5 (b) 0.0625

(c) 0.0039 (d) 0.75 (e) 0.25

3-73. (a) 0.0064 (b) 0.9984

(c) 0.008

3-75. (a) 0.0167 (b) 0.9224 (c) 50

3-77. (a) 3.91  10 ^19 (b) 200

(c) 2.56  1018

3-79. (a) 5 (b) 5

3-81. (a) 20 (b) 0.0436

(c) 0.0459 (d) 0.0411 (e) 19

3-83. (a) 3000 (b) 1431.18

Section 3-8

3-87. (a) 0.4623 (b) 0.0002

(c) 0.9866 (d)E(X)0.8,

V(X)0.539

3-89. F(X)0 for x0; 16 for 0 

x1; 23 for 1 x2; 29 30

for 2 x3; 1 for 3 x

3-91. (a) 0.1201 (b) 0.8523

3-93. (a) 0.7069 (b) 0.0607

(c) 0.2811

Section 3-9

3-97. (a) 0.0183 (b) 0.2381

(c) 0.1954 (d) 0.0298

3-99. E(X)2.996, V(X)2.996

3-101.(a) 0.0045 (b) 0.3679

(c) 0.1353 (d) 0.2642

3-103.(a) 4.54  10 ^5 (b) 0.6321

3-105.(a) 0.6065 (b) 8.9 10 ^5

(c) 0.00146

Supplemental

3-107.0.3714

3-109.(a) 0.0117 (b) 1.3333

3-111.(a) 0.1755 (b) 0.0858

(c) 0.2873

3-113.0.9810

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