17. (a) 0.0072 (b) 0.9921 (c) 0.0079(d) 0.0079 (e) 0.4;

19. (a) 0.1404 (b) 0.1247 (c) 0.8753 (d) 5;

21. (a)

2520.4

(b)

(c)

mX = 0.61

7.1 Exercises Answers AN-25

17. (a) 15. (a)

(d) The probabilities are very close to the relative frequencies, sothe random variable X appears to follow a Poisson distribution.

19. (a) and (b) 0.0506(c) 0.0429 (d) 0.0487; 0.0395

21. (a) 119

Chapter Review Exercises (page 371)

1. (a) Continuous,(b) Discrete, (assuming 91 days of winter)(c) Discrete, where n is the number of tee

shots hit3. No,

5. (a)

gP1X = x2 Z 1

x = 0, 1, 2, Á , nx = 0, 1, Á , 91

s Ú 0

np … 10n Ú 100

(b)

Number of Deaths, x Relative Frequency

0 0.55

1 0.33

2 0.11

3 0.02

4 0.01

Number of Deaths, x

0 0.5434

1 0.3314

2 0.1011

3 0.0206

4 0.0031

P1X � x2

x

4 0.3226

5 0.2419

6 0.2742

7 0.1613

P1X � x2

0.1

0.05

0.15

0.2

0

0.35

0.3

0.25

Number of Games54 76

Pro

babi

lity

Number of Games Necessary to Win the Stanley Cup

(c) (d)7. $29. Binomial experiment

11. (a) 0.4344 (b) 0.1478 (c) 0.1879(d) 0.3777 (e) 20; 4.3(f) No, because 12 is within two standard deviations of 20.(g) Yes, because the probability of observing four or more suc-

cesses if is 0.0058.(h) 0.0993

13. (a) 0.0022 (b) 0.9441 (c) 0.4417(d) 0.1250 (e) 37; 5.85(f) Yes, because 50 is more than two standard deviations from

the mean, 37.(g) No, because the probability of observing one or fewer suc-

cesses if is 0.3384.p = 0.074

p = 0.08

sX = 1.1mX = 5.3

x x

0 0.3277 3 0.0512

1 0.4096 4 0.0064

2 0.2048 5 0.0003

P1X � x2P1X � x2

(b) (c)

(d)

mX = 1; sX = 0.9mX = 1; sX = 0.9

x

P(X

� x

)

0 21 43 5

Binomial Probability Distribution

0.350.300.25

0.100.05

0.150.20

0.00

0.450.40

mx � 1

x

0 0.47237

1 0.35427

2 0.13285

3 0.03321

4 0.00623

P1X � x2

x

0 0.53125

1 0.28125

2 0.12500

3 0.03125

4 0.03125

P1X � x2

(b) 0.75

(c)

(d) The probabilities computed from the Poisson distributionare fairly close to the actual values. It seems reasonable touse the Poisson distribution to model the number of earth-quakes per year.

CHAPTER 7 The Normal ProbabilityDistribution

7.1 Exercises (page 388)

1. 1/6 3. 1/3

5. (a)

Den

sity

1

1 x

(b) 0.2 (c) 0.35(d) 0.05 (e) Answers will vary

7. Normal9. Not normal

11.13. m = 100, s = 15m = 2, s = 3

SullivanAns_SE_finpp1-49 11/20/02 4:33 PM Page 25

AN-26 Answers 7.4 Exercises

15. (a), (b) 23. (a) 4.28% (b) 8.98%25. (a) 63.4 inches (b) 69.8 inches (c) 58.6–69.6 inches27. (a) 170 (b) 146–17629. (a) 70° F (b) 94° F (c) 70° F–90° F

31. (a)

-7.48%;

33. (a)

(b)

505395 615

(c) (i) The proportion of SAT Verbal scores less than 395 is0.1587. (ii) The probability that a randomly selected stu-dent scored less than 395 on the SAT Verbal is 0.1587.

17. (a),(b)

34002895 3905 4410

(c) (i) The proportion of full-term babies that weigh more than4410 grams is 0.0228. (ii) The probability that a randomly se-lected full-term baby weighs more than 4410 grams is 0.0228.

19. (a) (i) The proportion of human pregnancies that last more than280 days is 0.1908. (ii) The probability that a randomly selectedhuman pregnancy lasts more than 280 days is 0.1908.

(b) (i) The proportion of human pregnancies that last between230 and 260 days is 0.3416. (ii) The probability that a ran-domly selected human pregnancy lasts between 230 and 260days is 0.3416.

21. (a) (b) 0.67 (c) 0.49523. (a)–(c) Answers will vary

7.2 Exercises (page 403)

1. (a) 0.0071 (b) 0.3336 (c) 0.9115 (d) 0.99983. (a) 0.9987 (b) 0.9441 (c) 0.0375 (d) 0.00095. (a) 0.9586 (b) 0.2088 (c) 0.84797. (a) 0.0456 (b) 0.0646 (c) 0.52039. (a) 0.8877 (b) 0.9802 (c) 0.0198

11. 13. 2.05 15. 0.6717. 19. 1.28 21. 2.57523. 1.645 25. 2.33 27. 0.8429. 0.9732 31. 0.9986 33. 0.875335. 0.0329 37. 0.7642 39. 0.087543. 0.0054 45. 0.1906

7.3 Exercises (page 411)

1. 0.9838 3. 0.2389 5. 0.9074 7. 0.2368 9. 0.717511. (a) 0.1492 (b) 0.901 (c) 0.2510

(d) 0.2743 (e) 0.2856(f) A little unusual, because the probability that a randomly se-

lected 20–29-year-old female would have a serum HDL lessthan 30 is 0.0427.

13. (a) 0.4761 (b) 0.6179 (c) 0.5714(d) A little unusual, because the proportion of monthly returns

greater than 9.7 percent is only 0.0166.15. (a) 7.21% (b) 0.24% (c) 91.05% (d) 0.9105

(e) A little unusual, because the proportion of 20–29-year-oldfemales who are more than 5 feet, 10 inches, is 0.0174.

17. (a) 14.46% (b) 27.09% (c) 33.52%(d) 0.1587 (e) 0.3208

19. (a) 10.56% (b) 0.62% (c) 25.81%(d) 0.1056 (e) 0.3413

21. (a) 44 (b) Exact (c) 35.8; 70.2

-2.575;-1.28;-1.23-1.28

-0.67

Theoretical Theoretical Score Proportion Score Proportion

200–249 0.0068 500–549 0.1709

250–299 0.0188 550–599 0.1491

300–349 0.0430 600–649 0.1072

350–399 0.0811 650–699 0.0636

400–449 0.1260 700–749 0.0311

450–499 0.1616 750–800 0.0127

Relative Relative Temperature Frequency Temperature Frequency

5.0–9.9 0.0005 40.0–44.9 0.2000

10.0–14.9 0.0053 45.0–49.9 0.1499

15.0–19.9 0.0080 50.0–54.9 0.1243

20.0–24.9 0.0213 55.0–59.9 0.0853

25.0–29.9 0.0507 60.0–64.9 0.0539

30.0–34.9 0.1157 65.0–69.9 0.0112

35.0–39.9 0.1733 70.0–74.9 0.0005

Temperature

Rel

ativ

e F

requ

ency

0.25

0.1

0.05

0.15

0.2

05 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Chicago Temperatures, Nov. 16–30

Temperature Theoretical Proportion

5.0–9.9 0.0006

10.0–14.9 0.0025

15.0–19.9 0.0090

20.0–24.9 0.0256

25.0–29.9 0.0586

30.0–34.9 0.1071

35.0–39.9 0.1567

40.0–44.9 0.1836

45.0–49.9 0.1721

50.0–54.9 0.1291

55.0–59.9 0.0776

60.0–64.9 0.0373

65.0–69.9 0.0143

70.0–74.9 0.0044

(c)

(d)

m = 43.5° F, s = 10.5° F

7.4 Exercises (page 421)

1. Not normal3. Normal5. Normal

SullivanAns_SE_finpp1-49 11/20/02 4:33 PM Page 26

7.6 Exercises Answers AN-27

7. Normal

9. Not normal

(c) The probability of obtaining a sample mean of 3.6 insectfragments or more is 0.0071. Since this result is unusual ifthe population mean is 3, we are inclined to believe that thepopulation mean is more than 3.

15. The probability of obtaining a sample mean of 68.3° F or higherfrom a population whose mean is 67.6° F is 0.1190.This is not anunusual result.

17. (a) The probability of obtaining a sample mean of $32,030 froma population whose mean is $45,127 is 0.0044. This result isunusual. We conclude that the population mean for house-holds in Cook County, IL is likely less than $45,127.

(b) No; since the median is less than the mean, the distributionis skewed to the right.

19. (a)(b) 98, 106; 98, 104; 98, 120; 98, 100; 98, 114; 106, 104; 106, 120;

106, 100; 106, 114; 104, 120; 104, 100; 104, 114; 120, 100; 120,114; 100, 114

(c)

m = 107

(d) (e)

(f)

P A102 … x … 112 B =1115

mx = 107

With the larger sample

size, the probability of obtaining a sample mean within fiveIQ points of the population mean has increased.

21. (a)–(c) Answers will vary. (d)

(e) Answers will vary. (f) 0.0125(g) Answers will vary.

23. Answers will vary.

7.6 Exercises (page 442)

1. Area under the normal curve to the right of 3. Area under the normal curve between and 5. Area under the normal curve between and 7. Area under the normal curve to the right of 9. 0.0616; 0.0618 11. 0.0677; 0.0630

13. (a) 0.0568 (b) 0.1469 (c) 0.0262 (d) 0.4142

X = 20.5X = 24.5X = 17.5

X = 8.5X = 7.5X = 39.5

mx = 100; sx =16220

mx = 107; P A102 … x … 112 B =45

;

7.5 Exercises (page 434)

1. 3.

5. (a) Approximately normal;

(b) 0.1469 (c) 0.0174 (d) 0.89217. (a) Population must be normal. is normal with

(b) 0.6406 (c) 0.1292

9. (a) 0.3015 (b) 0.0217 (c) 0.0096

(d) The larger the sample size, the lower is the probability. This isdue to the Law of Large Numbers.As the sample size increas-es, the standard error decreases. Therefore, as the sample sizeincreases, 60 is more standard errors from making 60 a lesslikely occurrence.

11. (a) 0.3520 (b) 0.0465 (c) 0.0040(d) Since the probability of obtaining a sample mean of 260 or less

from a sample of pregnancies is 0.004, we can con-clude one of two things: (i) We just happened to select 50 preg-nancies that had short gestation periods, or (ii) the populationmean is less than 266. Explanation (ii) would be reasonable ifour sample came from a specific population—say, “at-risk”women whose labor may have been induced for medical rea-sons and who therefore had a gestation period less than 266days. Since we do not have any indication that explanation (ii)is reasonable, we are inclined to believe explanation (i).

13. (a) Because the sample size, n, is large.

(b) mx = 3, sx =23250

n = 50

m,

sx =16210

.

mx = 105,x

mx = 50; sx =6240

mx = 100; sx =12220

mx = 50; sx =6240

Probability

99 1/15

101 1/15

102 2/15

103 1/15

105 1/15

106 1/15

107 1/15

109 2/15

110 2/15

112 1/15

113 1/15

117 1/15

x

Probability Probability

100.7 1/20 107.3 1/20

101.3 1/20 108 3/20

102.7 1/20 108.7 1/20

103.3 1/20 110 1/20

104 1/20 110.7 1/20

105.3 1/20 111.3 1/20

106 3/20 112.7 1/20

106.7 1/20 113.3 1/20

xx

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33. (a)

AN-28 Answers 8.1 Exercises

15. (a) 0.0072 (b) 0.9871 (c) 0.2296 (d) 0.012917. (a) 0.0077 (b) 0.9934 (c) 0.00281 (d) 0.014319. (a) 0.0506 (b) 0.0018 (c) 0.8665 (d) 0.001821. (a) 0.0089

(b) Either the proportion of males between 18 and 24 years ofage is higher than 59%, or the sample just happened to re-sult in a lot of 18–24-year-olds who live at home.

23. (a) 0.0032(b) Yes, assuming that our sampling was done appropriately, we

are inclined to believe that the proportion of respondentswho would prefer a boy is higher than 42%.

25. (a) 0.00764 (b) No

Chapter Review Exercises (page 445)

1. (a) 60 (b) 10(c) (i) The proportion of random variables to the right of

is 0.0668. (ii) The probability that a randomly se-lected random variable is greater than is 0.0668.

(d) (i) The proportion of random variables between andis 0.7745. (ii) The probability that a randomly selected

random variable is between and is 0.7745.3. (a) (b) 0.25 (c) 0.29125. 0.1492 7. 0.4816 9. 0.8830 11. 0.8756 13. 0.99

15. 1.75 17. 0.84 19. 0.2033 21. 0.624723. (a) 0.1271 (b) 0.0116 (c) 0.8613 (d) 60,980 miles

(e) Normal; (f )0.0359

(g) Normal; (h) 0.0023

25. (a) 0.4090 (b) 0.4692 (c) 0.2177 (d) 120(e) Yes, 144 (f) 0.3897 (g) 0.3264

27. (a) (b) 0.1000 (c) 0.1210(d) 0.6517 (e) 0.9868 (f) 0.6451

29. Not normal31. Not normal

np11 - p2 = 14.72 Ú 10

mx = 70,000; sx =4400225

mx = 70,000; sx =4400210

-1.75;

-0.5X = 75X = 50

X = 75X = 50

X = 75X = 75

(b)

(c)

(d)

m = 2929.1; s = 554.5

35. (a) Normal; (b) 0.0016

37. (a)

mx = 120; sx =172100

(b) 0.25 (c) 0.4

CHAPTER 8 Confidence Intervals about a Single Parameter

8.1 Exercises (page 466)

1. No 3. No 5. Yes 7. 2.33 9. 1.4411. (a) Lower bound: 32.44; Upper bound: 35.96

(b) Lower bound: 32.73; Upper bound: 35.67; the margin oferror decreases.

(c) Lower bound: 31.89; Upper bound: 36.51; the margin oferror increases.

(d) Only if the population is normal13. (a) Lower bound: 102.66; Upper bound: 113.34

(b) Lower bound: 99.56; Upper bound: 116.44; the margin oferror increases.

(c) Lower bound: 103.96; Upper bound: 112.04; the margin oferror decreases.

(d) No(e) The sample mean would increase, causing the interval to in-

clude larger values.15. (a) $542.25 (b) Yes

(c) Lower bound: $326.65; Upper bound: $757.85. The Insur-ance Institute is 95% confident that the mean cost of repairto a Chevy Cavalier crashed at 5 miles per hour is between$326.65 and $757.85.

(d) Lower bound: $361.32; Upper bound: $723.18. The Insur-ance Institute is 90% confident that the mean cost of repairto a Chevy Cavalier crashed at 5 miles per hour is between$361.65 and $723.18.

Birth Weight Relative Frequency

0–499 grams 0.00002

500–999 grams 0.00037

1000–1499 grams 0.00343

1500–1999 grams 0.03078

2000–2499 grams 0.17073

2500–2999 grams 0.36342

3000–3499 grams 0.29324

3500–3999 grams 0.10936

4000–4499 grams 0.02388

4500–4999 grams 0.00415

5000–5499 grams 0.00062

500 4500400035003000250020001000 1500 5000 5500Weight (grams)

Rel

ativ

e F

requ

ency

0.25

0.10

0.05

0.15

0.20

0.40

0.30

0.35

0.00

Birth Theoretical Birth Theoretical Weight Proportion Weight Proportion

0–499 grams 0.000006 3000–3499 grams 0.2971

500–999 grams 0.00024 3500–3999 grams 0.1248

1000–1499 grams 0.0047 4000–4499 grams 0.0244

1500–1999 grams 0.0418 4500–4999 grams 0.0022

2000–2499 grams 0.1721 5000–5499 grams 0.000092

2500–2999 grams 0.3306

y

x20

1 20

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