53. a.
Exact: .212, .577, .573; Approximate: .211, .567, .596
b.
Exact: .885, .575, .017; Approximate: .885, .579, .012
c.
Exact: .002, .029, .617; Approximate: .003, .033, .599
55. a.
.9409
b.
.9943
57. b.
Normal,
59. a.
1
b.
1
c.
.982
d.
.129
61. a.
.480, .667, .147
b.
.050, 0
63. a.
short plan 1 better, whereas long
plan 2 better
b. 65. a.
.238
b.
.238
c.
.313
d.
.653
e.
.653
f.
.713
67. a.
.424
b.
.567,
c.
60
d.
66
69. a. b.
Exponential with
c.
Exponential with parameter
73. a.
.826, .826, .0636
b.
.664
c.
172.727
77. a.
123.97, 117.373
b.
.5517
c.
.1587
79. a.
9.164, .385
b.
.8790
c.
.4247, skewness
d.
No, since P
81. a.
149.157, 223.595
b.
.9573
c.
.0414
d.
148.41
e.
9.57
f.
125.90
83. 85. b.
87.
Yes, since the pattern in the plot is quite linear.
89.
Yes
91.
Yes
93.
Plot lnx vs. z percentile. The pattern is straight, so a lognormal population distribution is plausible.
95.
The pattern in the plot is quite linear; it is very plausible that strength is normally distributed.
97.
There is substantial curvature in the plot. is a scale param- eter as is for the normal family.
s l
b a 1 b
[⌫a 1 b ⌫
m 1 b][⌫a 1 b 1 m ⌫
b], a 5 b
X , 17,000 5 .9332 nl
l 5 .05
¨ A
i
m | , 24
1l 5 15 1 E[h
1
X] 5 150, E[h
2
X] 5 138.51 1l 5 10 1 E[h
1
X] 5 100, E[h
2
X] 5 112.53 1
1 m 5
239, s
2
5 12.96
99. a.
for
b.
.259, .5, .241
c.
6, 43.2, 7.2
d.
.518
e.
3.75
101. a.
for and for
b.
.917
c.
1.213
103. a.
.9162
b.
.9549
c.
1.3374
105. a.
.3859
b.
.0663
c.
72.97, 119.03
107. b.
for for ,
and for
c.
No.
d. 109. a.
.368, .828, .460
b.
352.53
c. d.
e.
, mode
111. a. b.
No
c. d.
e. 113. b.
c. d.
e.
f. 115. a.
Lognormal
b.
1
c.
2.72, .0185
119. a.
Exponential with
c.
Gamma with parameters and
121. a.
1365
3
b.
1365
2
c.
.000002145
123. b.
Let be a sequence of observations from a
Unif[0, 1] distribution a sequence of random numbers. Then with
, the ’s are observa- tions from an exponential distribution with
.
125. 127. a.
710, 84.423, .684
b.
.376 g
EX EgX l 5
10 x
i
x
i
5 2.1ln1 2 u
i
u
1
, u
2
, u
3
, c
cb a
l 5 1
CV , 1
1, CV . 1 V
X 5 2pl
2 1
1 21 2 pl
2 2
2 m
2
p l
1
1 1 2 pl
2
for x 0 p
1 2 exp 2l
1
x 1 1 2 p1 2 exp 2l
2
x n 2
2 a 2 1b
m 5
150, m | 5 182.99
m 5 201.95
a 1b
exp [2exp 2x 2 ab] exp 2x 2 ab
Y | Bin10, 5
27 F
0 , .5 1 m | . 0
x . 2
5 1
2 1 x 2
x , 2 1, 5 4x 2 x
3
39 1 11
27 F
x 5 0 1 x
7 3
5 7
4 2
3 4
x 0 x , 1
f x 5 x
2
0 y 12 F
y 5 1
48 y
2
2 y
3
18
1. a.
.20
b.
.42
c.
At least one hose is in use at each pump; .70.
d. p
X
x .16, .34, .50 for x 0, 1, 2, respectively; p
Y
y .24, .38, .38 for y 0, 1, 2, respec- tively; .50
e.
No; p0, 0 ⬆ p
X
0 ⭈ p
Y
3. a.
.15
b.
.40
c.
.22
d.
.17, .46
5. a.
.054
b.
.00018
7. a.
.030
b.
.120
c.
.300
d.
.380
e.
Yes
9. a.
3380,000
b.
.3024
c.
.3593
d.
10Kx
2
⫹ .05 for 20 x 30
e.
No
11. a. ⭈ m
1 x
⭈ m
2 y
xy
b. ⭈
[1 ⫹ m
1
⫹ m
2
]
c. ⭈
m
1
⫹ m
2 m
m; Poisson m
1
⫹ m
2
13. a. e
⫺x ⫺ y
for x 0, y 0
b.
.400
c.
.594
d.
.330
15. a. F
y 1 ⫺ e
⫺ly
⫹ 1 ⫺ e
⫺ly 2
⫺ 1 ⫺ e
⫺ly 3
for y 0
b.
23l
17. a.
.25
b.
.318
c.
.637
d.
for ⫺R x R; no f
X
x 5 22R
2
2 x
2
pR
2
e
2 m
1
1 m
2
e
2m
1
2 m
2
e
2m
1
2 m
2
Chapter 5
Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook andor eChapters. Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
19. a.
K x
2
⫹ y
2
10Kx
2
⫹ .05; Kx
2
⫹ y
2
10Ky
2
⫹ .05
b.
.556, .549
c.
25.37, 2.87
21. a.
f x
1
, x
2
, x
3
f x
1
, x
2
b.
f x
1
, x
2
, x
3
f x
1
23.
.15
25.
L
2
27.
.25 hr
29. 31. a. ⫺
.1082
b. ⫺
.0131
37. a.
25 32.5 40 45 52.5 65
p .04
.20 .25 .12 .30 .09
b. s
2
112.5 312.5 800 p
s
2
.38 .20
.30 .12
39.
Proportion .1
.2 .3
.4 .5
Probability .000
.000 .000
.001 .005
.027 Proportion
.6 .7
.8 .9
1.0 Probability
.088 .201
.302 .269
.107
41. a.
1 1.5
2 2.5
3 3.5
4 p
.16 .24
.25 .20
.10 .04
.01
b.
.85
c. r
1 2
3 p
r .30
.40 .22
.08
47. a.
.6826
b.
.1056
49. a.
.6026
b.
.2981
51.
.7720
53. a.
.0062
b. 55. a.
.9838
b.
.8926 x
x x
x 2
2 3
X
1
X
1
, X
2
57.
.9616
59. a.
.9986, .9986
b.
.9015, .3970
c.
.8357
d.
.9525, .0003
61. a.
3.5, 2.27, 1.51
b.
15.4, 75.94, 8.71
63. a.
.695
b.
4.0675 . 2.6775
65. a.
.9232
b.
.9660
67.
.1588
69. a.
2400
b.
1205; independence
c.
2400, 41.77
71. a.
158, 430.25
b.
.9788
73. a.
Approximately normal with mean 105, SD 1.2649; Approximately normal with mean 100, SD 1.0142
b.
Approximately normal with mean 5, SD 1.6213
c.
.0068
d.
.0010, yes
75. a.
.2, .5, .3 for x 12, 15, 20; .10, .35, .55 for y 12, 15, 20
b.
.25
c.
No
d.
33.35
e.
3.85
77. a.
381,250
b. f
X
x k250x ⫺ 10x
2
for 0 x 20 and
for 20 , x 30; f
Y
y results from substituting y for x in f
X
x. They are not independent.
c.
.355
d.
25.969
e.
204.6154, ⫺.894
f.
7.66
79.
1
81. a.
400 min
b.
70
83.
97
85.
.9973
89. b
, c. Chi-squared with n n.
91. a. b.
.9999
93.
26, 1.64
95. a.
.6
b. U 5 rX 1 2
1 2 r
2
Y s
W 2
s
W 2
1 s
E 2
5 k 450x 2 30x
2
1
1 2
x
3
, E m 44.5 X
, ES
2
212.25 s
2
Chapter 6
1. a.
8.14,
b.
.77,
c.
1.66, S
d.
.148
e.
.204, S
3. a.
1.348,
b.
1.348,
c.
1.781, ⫹ 1.28S
d.
.6736
e.
.0846
5.
N 1,703,000;
T ⫺ N 1,591,300;
T ⭈
1,601,438.281
7. a.
120.6
b.
1,206,000
c.
.80
d.
120.0
9. a.
2.11
b.
.119
11. b. c.
Use
i
x
i
n
i
and
i
1 ⫺
i
in place of p
i
and q
i
in part b for i 1, 2.
d. ⫺
.245
e.
.041
15. a. b.
74.505 uˆ 5
gX
i 2
2n pˆ
qˆ pˆ
c p
1
q
1
n
1
1 p
2
q
2
n
2
d
12
y x
d x
X X
X X
X |
X
17. b.
.444
19. a. b.
21. b. 23.
, estimate of m
1
⫺ m
2
is ⫺ .
25. a.
384.4, 18.86
b.
415.42
29. a. b.
.64, .202
33.
With x
i
time between birth i ⫺ 1 and birth i, .
35.
29.5
37.
1.0132 l
ˆ 5 6 a
6 i5
1
ix
i
5 .0436
uˆ 5 min X
i
, lˆ 5 n g[X
i
2 min X
i
] y
x m
ˆ
1
5 x , mˆ
2
5 y a
ˆ 5 5, bˆ 5 28.0⌫1.2 pˆ 5
100lˆ 2 970 pˆ 5
2lˆ 2 .30 5 .20
Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook andor eChapters. Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
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