Johnson7e
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7:45 P.M.
0
CHAPTER 1
D
1.3
The statistical population is, for all males
in US, the decision to buy flowers that
day or day before, or, not buy at that
time. The sample is the choices of the
451 males where 144 do purchase at that
time.
Sample is the 20 numbers of close friends
recorded. Statistical population is the
collection of numbers from all college
students.
The statistical population is collection
of responses not more/more stressed for
all 20-25 year olds in country. Sample is
collection of 40 responses reported.
No. Likely to be among heavy drug users.
(a) Sample.
(b) Anecdotal.
Comfortable not well defined. Could
require majority of sample to rate as 5
on a five-point scale.
Lab, receptionist, and X-ray.
Population: Entire set of responses
from all U.S. teens 13 to 17. Sample:
Responses from the 1055 teens contacted.
R
1.1
AF
T
Answers to Selected
Odd-Numbered Exercises
1.5
1.7
1.9
1.13
1.17
1.19
1.21
1.23
1.25
1.27
1.29
(a) Person living in Chicago.
(b)
Whether a person is a registered voter
(yes) or not (no).
(c) Entire set of
yes/no responses from all persons living
in Chicago.
(a) Anyone who golfs.
(b) The
statistical population is the collection of
estimated hole sizes, one for each golfer.
The sample is the collection of 46 hole
sizes the psychologists recorded.
It is likely that any person visiting the site
does so because they have a problem with
procrastination. The scores recorded
would not be representative of the general population.
Population: The entire collection of
responses, from all residents, of their
favorite establishment. Sample: The
responses from the persons who filled
out the form. This is a self-selected
sample, and not representative, as only
those with strong opinions would fill
out form.
(a) Anecdotal.
(b) Sample based.
(c) Sample based.
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ANSWERS TO SELECTED ODD-NUMBERED EXERCISES
1.31
1.37
“Too long” is not well defined. Could, for
instance, say half the time it takes longer
than 5 minutes.
(b) Including votes only from those
with strong enough opinions to call in,
like big dogs jumping above the fence,
would produce unrepresentative results.
2.25
0
1
1
2
2
2.27
CHAPTER 2
2.3
2.5
2.7
2.9
2.11
2.13
2.17
2.19
Frequency
R
Class
D
0.45–0.90
0.90–1.35
1.35–1.80
1.80–2.25
2.25–2.70
2.21
2.23
2
6
11
5
6
The frequencies are 12, 16, 10, 11, and 8.
The classes are not of equal length.
The stem-and-leaf display:
2.29
0
1
2
3
4
5
The double-stem display:
3
3
4
4
5
6
22344
55567777889
00000022244
5567799
022444
566
11
67
12
The five-stem display Leaf Unit = 1.0
20
20
20
20
20
21
21
21
21
21
22
22
22
22
22
23
23
23
23
23
24
24
24
24
24
25
25
(a) 22.8%
(c) 28.5%, 42.4%,
77.2%
The frequencies are 7, 10, 13, 5, 2, 1, 1,
1.
(a) The relative frequencies are Drive
alone .625, Car pool .075, Ride bus .175,
and Other .125.
3 belongs to two classes.
5 doesn’t belong to any class.
(a) Yes.
(d) No.
(e) No.
(c) 9 / 50 = .18
(c) 1 / 15 = .067
(a) The frequency table
695
0
2
AF
T
2.1
7:45 P.M.
6
2234455567777889
000000222445567799
022444566
1167
12
2.31
2.33
2.35
89
011
2
4
7
99
0
55
1
2333
44
8
3
(a) Median = 3 and x = 3
(c) Median = −1 and x = −1
(b) Median since
(a) x = 254
one large observation heavily influences
the mean.
Claim ignores variability. July with 105 is
hot.
(b) Either
(a) x = 8.48
Page 695
Johnson7e
2.39
2.43
2.45
2.47
2.49
2.51
2.53
2.57
2.59
2.63
2.65
2.67
2.71
2.73
D
2.75
2.77
2.81
Mean = 118.05 is center where sum
of positive deviations balance the sum of
negative deviations. Median = 117.00
has at least half of weights the same or
smaller and at least half the same or
larger.
(a) 2.60
(b) 2.00
181.5
(b) x = 26.62 sample median = 24
(c) Q1 = 22, Q2 = 24,
and Q3 = 30
(a) Sample median = 153
(b) Q1 = 135.5, and Q3 = 166.5
Sample median = 94, Q1 = 73, and
Q3 = 105
(a) Median = 110, Q1 = 60,
Q3 = 340
(b) 90th percentile = 400
(b) Mean = 24.33◦ C, median =
24.44◦ C
(b) s2 = 7 and s = 2.646
(b) s2 = 18.667 and s = 4.32
(c) s2 = .286
(a) s2 = 1.30
(a) s = 139.48
(b) Reduces to almost half.
(a) s2 = 155, 226
(b) s = 393.99
(a) Median = 68.4
(c) s = 2.419
(b) x = 68.343
(b) 25.00
(a) s2 = 239.32
(c) 8 is nearly half as variable.
Interquartile range = 31.0
No. Extremes more variable than middle.
(a) x = 2.600 and s = 1.303
(b) Proportions .5, 1.0, and 1.0, respectively.
(a) −1.037
(b) 1.677
(a) Mean = 21.92, standard deviation
= 5.405
(b) 22 / 24 = .917
Mean = 1.925, standard deviation =
1.607
(a) 20.5
(b) Maximum 63 and
minimum − 8 (gain) Bush.
(c)
71 Obama
Only the value 215 from the second
period is outside of limits.
2.83
2.87
2.89
2.91
2.95
2.97
7:45 P.M.
2.99
First an upward trend and then a downward trend. Control limits not appropriate.
(a) The relative frequencies of the
occupation groups are:
Occupation
Relative Frequency
Group
2010
2000
Goods producing
Service (private)
Government
.117
.730
.148
.161
.702
.136
Total
1.000
.999
AF
T
2.37
V2 - 09/27/2013
ANSWERS TO SELECTED ODD-NUMBERED EXERCISES
R
696
b02.tex
2.103 (a) Yes.
(b) Yes.
(c) No.
2.105 (a) Mean = 227.4 pounds is center
where sum of positive deviations balance the sum of negative deviations.
Median = 232.5 has at least half of
weights the same or smaller and at least
half the same or larger.
(b) 82.7
(c) 1.120
2.107 (a) Median = 9
(b) x = 9.033
(c) s2 = 3.895
2.109 (a) x = 7, s = 2
(c) Mean = −21, standard
deviation = 6.
2.113 (a) x = 5.375 and s = 3.424
(b) Median = 5.0
(c) Range = 13
2.115 (a) Median = 4.505, Q1 = 4.30,
Q3 = 4.70
(b) 4.935
(c) x = 4.5074, s = .368
2.117 (a) Median = 6.7, Q1 = 6.4,
Q3 = 7.1
(b) x = 6.74 and s = .463
2.119 (b) Not reasonable with time trend.
2.121 Mean = 80.30 and standard
deviation = 39.30
2.129 (b) x = 109.1, s = 65.8
Page 696
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ANSWERS TO SELECTED ODD-NUMBERED EXERCISES
CHAPTER 3
3.55
3.57
3.1
3.59
3.61
(c) The pill seems to reduce the proportions of severe and moderate nausea.
The proportion who study more than 10
hours is highest for the physical sciences.
It is .70 while social sciences have the
lowest proportion .48.
Relative Frequencies
3.3
3.7
Major
H
Male
.245
.082
Female
.122
0
Total
.367
.082
3.15
3.17
3.19
3.21
Total
.102
.286
.715
.082
.082
.286
.184
.368
1.001
(b) Research hospital best for either
condition.
(b) Positive—better players are paid
more.
No. Can only conclude there is not a
straight line relationship.
(b) r = −.415
(a) Figure (c)
(b) Figure (b)
(c) Figure (a)
r = −.578
r = .822
(b) r = .279
(b) r = .978
(b) 16 or more
0 = .52 β
1 = .70
(c) β
1 = 1.085
(a) β0 = 2.143 β
(b) y = −147.3 + 1.343x
(c) Relative Frequencies
D
3.23
3.25
3.27
3.33
3.37
3.39
3.41
3.43
3.47
S
R
3.11
P
CHAPTER 4
4.1
4.3
4.5
4.7
4.9
4.11
4.13
4.15
4.17
4.19
4.21
4.23
2-Wheel
3.49
3.51
3.53
4-Wheel
Total
.343
.657
1.000
.444
.556
1.000
(a) Negative. Only so much time.
(c) No relation.
No. Size of fire is a major lurking variable.
(b) r = −.313
697
(c) y = 1.15 + .37x
(a) x = road roughness and y =
gas consumption
(b) r = .649
(b) r = .437
(a) (iv)
(d) (vi)
(f) (i)
(a) (ii)
(b) (iii)
(a) { 0, 1 }
(b) { 0, 1, . . . , 344 }
(c) { t : 90 < t < 425.4 }
(a) S = { BJ, BL, JB, JL, LB, LJ,
BS, JS, LS, SB, SJ, SL }
(b) A = { LB, LJ, LS }
B = { JL, LJ, JS, SJ, LS, SL }
.1
(a) Yes.
(b) No, because the total is less than 1.
(c) Yes.
.2
.804
3
(c)
8
(a) S = { e1 , e2 , e3 } where ei =
2
[ the ticket has number i ]; P ( e1 ) = ,
8
3
3
P ( e2 ) = , P ( e 3 ) =
8
8
5
(b)
8
5
1
(c) P ( A ) =
, P( B ) = ,
36
6
1
1
P( C ) = , P( D ) =
2
6
4
(b)
9
11
12
1
(b)
(c)
(a)
15
15
15
S = { N, YN, YYN, YYYN, YYYYN,
YYYYY }
1
(b)
7
1
1
(b) P ( A ) = , P ( B ) =
2
3
AF
T
B
7:45 P.M.
4.25
4.27
4.29
4.33
Page 697
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7:45 P.M.
ANSWERS TO SELECTED ODD-NUMBERED EXERCISES
(b) (i) AB = { e6 , e7 }
(iii) AB = { e4 , e5 }
4.37 (b) AB = { e2 , e6 , e7 },
P ( AB ) = .41
(d) A C =
{ e3 , e4 }, P ( A C ) = .22
4.39 (b) A ∪ B = { e1 , e3 , e4 }, AB =
{ e3 }
4.41 (a) P ( A ) = .30 and P ( B ) = .36
(c) P ( A ∪ B ) = .40
4.43 (b) P ( AB ) = .18, P ( AB ) = .32,
P ( AB ) = .37
4.45 (b) P ( AB ) = .36
(c) P ( A ∪ B ) = .73
(d) .59
4.47 (a) P ( A ) = .65
(b) P ( AB ) = .15
7
4.49
18
4.51 (a) P ( B ) = .35
4.55 Reasonable to assume P ( A | B ) >
P ( A ). Dependent.
4.57 P ( B | A ) = .0099, dependent.
4.61 (a) P ( A ) = .4, P ( B ) = .4
(b) Dependent because P ( AB ) =
.1 = P ( A ) P ( B )
(c) P ( A ) =
P ( B ) = .4, independent.
4.63 (a) .1686 = 2073 / 12299
(b) .1988 = 1032 / 5192
4.65 (a) 688
(c) 769
2
7
4.67 (a)
(b)
9
12
4.69 (a) BC, P ( BC ) = 0
(c) B, P ( B ) = .8
4.71 .99991
4.73 (b) .896
4.75 (a) .55
(b) Yes.
4.77 (a) P ( B | A ) = .320
4.79 (b) 4.8%
(c) .360
4.81 (a) .8426
(b) .4488
4.83 (a) .058
(b) .362
4.85 (a) 210
(b) 90
4.87 (a) 462
(b) 210
4.91 (a) .491
(b) .084
4.93 No.
4.97 (a) .018
(b) .393
4.99 (a) 330
(b) .182
4.105 (a) A = { 23, 24 }
(d) A = { t : 0 ≤ t < 500.5 }
4.107 A = { p : .10 < p < 100 }, p is percent.
4.109 (a) .5
(b) .75
(c) .167
4.111 .5
4.113 (a) No.
(b) Yes.
(c) No.
4.115 (a) Either a faulty transmission or faulty
brakes or both.
(b) Transmission,
brakes, and exhaust system all faulty.
4.117 P ( A ) = .3, P ( AB ) = .10,
P ( A ∪ B ) = .5
4.121 (a) .25
(b) .76
4.123 (a) .25
(c) .34
4.125 P ( A | B ) = .8, they are independent.
4.127 (a) P ( A ) P ( C ) = .15, P ( AC ) =
.15, independent.
(b) P ( A B ) P ( C ) = .1,
P ( A B C ) = .15, dependent.
4.129 (a) .44
(b) .3846
(c) Dependent.
4.131 (a) .00008
(b) .00002
4.133 (a) .001312
(b) .000719
(c) .000801
(d) .228
4.135 (b) (ii) .64
(c) (iii) .49
1
4.137
= .0061
165
4.139 (a) .108
(b) .515
4.141 (a) .008
D
R
AF
T
4.35
CHAPTER 5
5.1
5.3
(a) Discrete.
(b)
(c) Continuous.
(a)
Possible Choices
{ 1,
{ 1,
{ 1,
{ 1,
{ 3,
{ 3,
{ 3,
{ 5,
{ 5,
{ 6,
3}
5}
6}
7}
5}
6}
7}
6}
7}
7}
Continuous.
x
2
4
5
6
2
3
4
1
2
1
Page 698
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ANSWERS TO SELECTED ODD-NUMBERED EXERCISES
(b)
x
f(x)
5.9
5.13
(a)
1
2
3
4
5
6
.2 .3 .1 .2 .1
.1
x
4
5
6
7
8
f(x)
.1
.4
.1
.2
.2
1
2
3
4
Total
5.49
f(x)
0
1
6
2
6
3
6
1
5.51
x
0
f(x)
1
4
x
0
1
1
2
1
2
1
4
2
3
4
R
(b) .5
f ( 2 ) = .2, f ( 4 ) = .2, f ( 6 ) = .2
(a) .94
(b) .47
(c) .41
(a) .45
(b) .25
(c) The capacity must be increased by 2
to a total of 4.
(b) E( X ) = 3, σ = 1
$931.20
μ = 2.4, σ = .980
(c) $228,500 with prep cost
(a) E( X ) = 1.381
(b) σ = 1.318
(b)
D
5.29
5.31
5.33
5.35
5.37
5.41
x
0
1
2
3
4
Total
f ( x ) .2401 .4116 .2646 .0756 .0081 1.0000
(c) E ( X ) = 1.2
5.59
5.61
5.63
f ( x ) .4096 .4096 .1536 .0256 .0016
5.19
5.21
5.25
5.27
5.53
5.55
5.57
5.65
5.69
5.71
5.73
5.75
5.77
5.79
5.81
5.83
5.85
5.87
5.89
5.91
5.93
699
Median = 3
(a) Trials are dependent.
(c) Bernoulli model plausible.
Identify S = yellow, F = other colors.
(a) Yes, p = .48
(b) No.
(c) No.
(a) Yes, P ( S ) = .5
(b) Dependent.
(a) Bernoulli trials model is not appropriate.
(b) Appropriate.
(a) .2401
(b) .0081
(a) .03456
(b) .3456
(c)
x
0
1
2
AF
T
5
1
1
2
0
3
3
3
Not a probability distribution; f ( 2 ) is
negative.
−
f(x)
5.17
5.47
x
Yes, a probability distribution.
(b)
2
3
4
x
5.15
5.43
5.45
7:45 P.M.
f(x)
81
256
f(x)
.400
126
49
256
256
1
(a) Yes, n = 10, p =
6
(b) No, because the number of trials is
not fixed.
(b) .132
(a) .9850
(b) .1265
(c) .3255
(a) .7383
(b) .6836
(c) 3
(a) .233
(b) .014
(c) .014
(a) .837
(b) .901
(a) Mean = 15 and sd = 1.936
(c) Mean = 12 and sd = 2.898
.411
Mean = 272.5, sd = 11.67
(b) Mean = 12.308, sd = 2.919
(a) P [ X ≤ 4 or X ≥ 13 ] = .072
(b) P [ X ≤ 3 or X ≥ 12 ] = .07
(c) The proportions for all resturants
are “in control”.
(a) .157
(b) .109
(c) .202
(a) .217
(c) .083
(a) .101
(c) .073
(a) .5221
(b) .478
(c) .474
(b)
x
0
1
2
.467
.133
Page 699
Johnson7e
5.95
(a) The probability distribution is given
in the first two columns.
0
1
2
3
Total
(b)
5.97 (a)
5.99 (a)
5.101 (a)
35
120
63
120
21
120
1
120
0
.525
.525
.350
.7
.025
.075
.9
1.3
x
0
1
3
f(x)
2
6
3
6
1
6
5
15
−15
6.1
6.3
0
−5
R
x
CHAPTER 6
6.5
1.00
(b) 1.0
5.105 (a)
x f ( x ) x2 f ( x )
f(x)
μ = .9 and σ 2 = .49
μ = 1.0 σ 2 = .6
.002
(b) −$0.60
.30
(b) σ = 1.342
5.103 (a)
6.9
6.11
6.13
6.15
6.17
6.19
6.21
6.23
6.25
6.27
6.29
6.31
6.33
6.35
6.37
6.41
f ( x ) .1458 .3936 .3543 .1063
(b) −$0.79
(c) No.
(a) F ( 3 ) = .44, F ( 4 ) = .72,
F ( 5 ) = .90, F ( 6 ) = 1.00
(b) Plausible.
(c) Does not apply.
.125
.140
(a) Binomial distribution with n =
6, p = .4
(b) .821, .047, 2.4
(b) 1.759
(c) .221
P [ X ≤ 10 ] = .048. This small probability casts doubt on the claim that
p = .7
(d) E( X ) = 2.0 and Var( X ) = 1.2
P [ X ≥ 10 ] = .048,
P [ X = 10 ] = .031
(a) .598
(c) μ = 3.2 and
σ = 1.6
(b) .180
(c) .156
D
5.109
5.111
5.113
5.115
5.117
5.119
5.121
5.123
5.125
5.127
7:45 P.M.
ANSWERS TO SELECTED ODD-NUMBERED EXERCISES
x
5.107
V2 - 09/27/2013
(c) Probability density function.
The interval 1.5 to 2 has higher probability.
Median = 1.414
X − 161
(c) Z =
5
X − 90
(b) Z =
12
(a) .7357
(c) .1515
(c) .8907
(d) .0510
(b) .8164
(d) .0695
(a) z = −.842
(c) z = .97
(a) z = −.93
(d) z = .753
(a) .6293
(d) z = 1.881
(a) .3446
(c) .2119
(e) .9093
(a) b = 67.64
(a) .0668
(c) .9198
.8468
.2024
(a) .0334
(a) (iii) .3830
(b) 16.5 to 17.5
(a) With continuity correction .2105.
(c) With continuity correction .8976.
No. n ( 1 − p ) = 2.4 small.
(a) .0923
(b) .0728
.2784 using continuity correction
.600 no continuity correction
Large values of volume are too large for
normal distribution.
Approximately a straight line pattern.
Normal distribution reasonable.
(a) Smallest values not small enough
and largest a little too large for normal
distribution.
(b) Normal distribution is reasonable
for the fourth root.
(a) 0.5
(b) First quartile =
.25, second quartile = .5, and third
quartile = .75
(a) z = −1.38
(c) z = .64
(a) .2676
(c) .0026
AF
T
700
b02.tex
6.43
6.47
6.49
6.51
6.55
6.57
6.59
6.61
6.65
6.67
Page 700