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
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