Applied Statistics and Probability for Engineers

APPENDIX C 681

3-115.

x 23456

f(x) 0.0025 0.01 0.03 0.065 0.13

x 78910

f(x) 0.18 0.2225 0.2 0.16

3-117. 299

3-119.(a) 4.1  10 ^5 (b) 10

(c) 0.9995

3-121.(a) 0.6 (b) 0.8 (c) 0.7

(d) 3.9 (e) 3.09

3-123.(a) 0.2408 (b) 0.4913

3-125.(a) 0.3233 (b) 0.0916

3-127.0.0738

3-129.(a) 0.3679 (b) 50.51

(c) 0.9234

CHAPTER 4

Section 4-2

4-1. (a) 0.3670 (b) 0.2858 (c) 0

(d) 0.9817 (e) 0.0498

4-3. (a) 0.4375 (b) 0.7969

(c) 0.5625 (d) 0.7031

(e) 0.5

4-5. (a) 0.5 (b) 0.4375 (c) 0.125

(d) 0 (e) 1 (f ) 0.9655

4-7. (a) 0.5 (b) 49.8

4-9. (a) 0.10 (b) 2.5

Section 4-3

4-11. (a) 0.56 (b) 0.7 (c) 0 (d) 0

4-13. 1 exfor x 0

4-15. 1 e(x4)for x 4

4-17. (a) 1.25x93.25 for

74.6 x75.4 (b) 0.5

4-21. F(x)0 for x0; 0.25x^2 for

0 x2; 1 for x 2

Section 4-4

4-23. E(X)2.6667, V(X)0.8889

4-25. E(X)4.083, V(X)0.3291

4-27. (a)E(X)109.39 m,

V(X)33.19 m^2

(b) $54.70

4-29. (a)E(X)5.1 mm, V(X)

0.01 mm^2 (b) 0.3679

Section 4-5

4-31. (a)E(X)3.5, V(X)1.33,

(^) X1.155 (b) 0.25
4-33. (a)E(X)50, V(X)0.0208,
(^) X0.144 (b)F(x) 2 x
99.5 for 49.75 x50.25
(c) 0.7
4-35. (a)E(X)1.85 min, V(X)
0.0408 min^2 (b) 0.7143
(c)F(x)(x1.5)0.7 for
1.5 x2.2
4-37. (b) 0.25 (c) 0.2140
(d)E(X)0.2100 m,
V(X)0.00000833 m^2
Section 4-6
4-39. (a) 0.90658 (b) 0.99865
(c) 0.07353 (d) 0.98422
(e) 0.95116
4-41. (a) 1.28 (b) 0 (c) 1.28
(d)1.28 (e) 1.33
4-43. (a) 0.93319 (b) 0.69146
(c) 0.9545 (d) 0.00135
(e) 0.15866
4-45. (a) 0.93319 (b) 0.89435
(c) 0.38292 (d) 0.80128
(e) 0.54674
4-47. (a) 0.99379 (b) 0.13591
(c) 5835
4-49. (a) 0.0082 (b) 0.72109
(c) 0.564
4-51. (a) 0.00135 (b) 0.15866
(c) 71.6 min
4-53. (a) 0.02275 (b) 0.47725
(c) 0.336
4-55. (a) 0.15866 (b) 90.0
(c) 99.73%
4-57. (a) 0.15245 (b) 125.6
4-59. (a) 0.06681 (b) 0.86638
(c) 0.000214
Section 4-7
4-61. (a) 0.075 (b) 0.85
4-63. (a) 0.129 (b) 0.488
4-65. 0.013
4-67. 0.966
4-71. (b) 330 (c) 0.0089
Section 4-9
4-73. (a) 0.3679 (b) 0.1353
(c) 0.0498 (d) 29.96
4-75. (a) 0.333 min (b) 0.333 min
(c) 0.9986
4-77. (a) 0.1353 (b) 0.4866
(c) 0.2031 (d) 34.54
4-79. (a) 0.0498 (b) 0.8775
4-81. (a) 0.0025 (b) 0.6321
4-83. (a) 0.1353 (b) 0.2707 (c) 5
4-85. (a) 0.2212 (b) 0.2865
(c) 0.2212
4-87. 0.8488
4-93. (a) 5 (b) 0.1353 (c) No
(d) 11.51
Section 4-10
4-97. (a) 0.1755 (b) 0.2643
4-99. (a) 50,000 (b) 0.677
4-101.(a) 500,000 (b) 223607
(c) 0.0803
4-103.(a) 0.1429 (b) 0.1847
4-105.(a) 120 (b) 1.32934
(c) 11.6317
Section 4-11
4-109.(a) 12,000 (b) 3.61  1010
4-111.(a) 0.5273 (b) 8862.3
(c) 0.00166
4-113.(a) 0.275 (b) 0.685
4-115.(a) 443.11 (b) 53650.5
(c) 0.2212
Section 4-12
4-117.(a) 0.9332 (b) 20952.2
(c)E(X)13359.7,
V(X)1.45  1012
4-119.(a) 0.983 (b) 0.45
4-121.
3.45, 2 2.25
Supplemental
4-125.0.25x^2 x 1 for 2 x 4
4-127.(a) 0.3935 (b) 0.3834
(c) 23.03
4-129.(a) 0.423 (b) 50
4-133.(a)
3.43, 2 0.96
(b) 0.946
4-135.(a) 0.6915 (b) 0.683
(c) 1.86
4-137.(a) 0.0062 (b) 0.0124
(c) 5.33
4-139.0.0008 to 0.0032
4-141.11,398
4-143.(a) 0.5633 (b) 737.5
4-145.(a) 0.984 (b) 0.834
CHAPTER 5
Section 5-1
5-1.
5-3. E(X)1.8125,
E(Y)2.875
5-5. c 1  36
5-7. E(X)2.167 , V(X)0.639,
E(Y)2.167, V(Y)0.639
f 1 x, y 2
0, g f 1 x, y 2  1
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