Chapters 6&7 practice

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In class Assignment Chapter 6 & 7

Name_____________________________________________________Date:

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Using the following uniform density curve, answer the question.

1) What is the probability that the random variable has a value greater than 5?

A) 0.325 B) 0.250 C) 0.500 D) 0.375

1)

2) What is the probability that the random variable has a value less than 6?

A) 0.625 B) 0.500 C) 0.875 D) 0.750

2)

3) What is the probability that the random variable has a value greater than 1.3?

A) 0.7125 B) 0.7875 C) 0.9625 D) 0.8375

3)

4) What is the probability that the random variable has a value between 0.4 and 0.8?

A) 0.3 B) 0.05 C) 0.075 D) 0.175

4)

Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.

5)

z -3.39 -2.26 -1.13 1.13 2.26 3.39 z -3.39 -2.26 -1.13 1.13 2.26 3.39

A) 0.1292 B) 0.8907 C) 0.8708 D) 0.8485

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6)

z -2.95-2.36-1.77-1.18-0.59 0.59 1.18 1.77 2.36 z -2.95-2.36-1.77-1.18-0.59 0.59 1.18 1.77 2.36

A) 0.2190 B) 0.7224 C) 0.2224 D) 0.2776

6)

7)

z

-1.82 1.82 z

-1.82 1.82

A)-0.0344 B) 0.4656 C) 0.9656 D) 0.0344

7)

8)

z

-1.84 -0.92 0.92 1.84 z

-1.84 -0.92 0.92 1.84

A) 0.3576 B) 0.8212 C) 0.1788 D) 0.6424

8)

Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.

9) Shaded area is 0.9599.

zz

A) 1.03 B) 1.75 C) 1.82 D)-1.38

9)

zz

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zz

A) 0.5557 B) 0.8051 C)-1.08 D) 1.08

11)

If z is a standard normal variable, find the probability. 12) The probability that z lies between 0 and 3.01

A) 0.4987 B) 0.1217 C) 0.5013 D) 0.9987

12)

13) The probability that z is less than 1.13

A) 0.8708 B) 0.8485 C) 0.8907 D) 0.1292

13)

14) The probability that z lies between -1.10 and -0.36

A) 0.2237 B)-0.2237 C) 0.4951 D) 0.2239

14)

15) P(z > 0.59)

A) 0.2190 B) 0.2224 C) 0.2776 D) 0.7224

15)

16) P(-0.73 < z < 2.27)

A) 0.4884 B) 0.7557 C) 0.2211 D) 1.54

16)

17) P(z < 0.97)

A) 0.1660 B) 0.8078 C) 0.8315 D) 0.8340

17)

18) The probability that z is greater than -1.82

A) 0.0344 B) 0.9656 C)-0.0344 D) 0.4656

18)

Assume that X has a normal distribution, and find the indicated probability.

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20) The mean is μ = 15.2 and the standard deviation is σ = 0.9. Find the probability that X is greater than 15.2.

A) 1.0000 B) 0.5000 C) 0.0003 D) 0.9998

20)

21) The mean is μ = 15.2 and the standard deviation is σ = 0.9.

Find the probability that X is between 14.3 and 16.1.

A) 0.8413 B) 0.1587 C) 0.6826 D) 0.3413

21)

Find the indicated probability.

22) The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater than 0.32 inches?

A) 37.45% B) 2.28% C) 47.72% D) 97.72%

22)

23) The incomes of trainees at a local mill are normally distributed with a mean of $1100 and a standard deviation of $150. What percentage of trainees earn less than $900 a month?

A) 9.18% B) 90.82% C) 40.82% D) 35.31%

23)

24) A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the probability of a rating that is between 200 and 275.

A) 0.4332 B) 0.5 C) 0.0668 D) 0.9332

24)

25) The weekly salaries of teachers in one state are normally distributed with a mean of $490 and a standard deviation of $45. What is the probability that a randomly selected teacher earns more than $525 a week?

A) 0.1003 B) 0.7823 C) 0.2177 D) 0.2823

25)

26) The diameters of pencils produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. What is the probability that the

diameter of a randomly selected pencil will be less than 0.285 inches?

A) 0.0596 B) 0.0668 C) 0.9332 D) 0.4332

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27) The lengths of human pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. What is the probability that a pregnancy lasts at least 300 days?

A) 0.9834 B) 0.4834 C) 0.0166 D) 0.0179

27)

28) Assume that the weights of quarters are normally distributed with a mean of 5.67 g and a standard deviation 0.070 g. A vending machine will only accept coins weighing between 5.48 g and 5.82 g. What percentage of legal quarters will be rejected?

A) 0.0196% B) 2.48% C) 1.62% D) 1.96%

28)

Solve the problem.

29) The amount of snowfall falling in a certain mountain range is normally distributed with a mean of 70 inches, and a standard deviation of 10 inches. What is the probability that the mean annual snowfall during 25 randomly picked years will exceed 72.8 inches?

A) 0.0026 B) 0.4192 C) 0.0808 D) 0.5808

29)

30) The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 109 inches, and a standard deviation of 10 inches. What is the probability that the mean annual precipitation during 25 randomly picked years will be less than 111.8 inches?

A) 0.9192 B) 0.5808 C) 0.0808 D) 0.4192

30)

31) The weights of the fish in a certain lake are normally distributed with a mean of 20 lb and a standard deviation of 9. If 9 fish are randomly selected, what is the probability that the mean weight will be between 17.6 and 23.6 lb?

A) 0.4032 B) 0.3270 C) 0.6730 D) 0.0968

31)

32) Assume that women's heights are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. If 90 women are randomly selected, find the probability that they have a mean height between 62.9 inches and 64.0 inches.

A) 0.1739 B) 0.7248 C) 0.0424 D) 0.9318

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33) For women aged 18-24, systolic blood pressures (in mm Hg) are normally distributed with a

mean of 114.8 and a standard deviation of 13.1. If 23 women aged 18-24 are randomly

selected, find the probability that their mean systolic blood pressure is between 119 and 122.

A) 0.0833 B) 0.3343 C) 0.9341 D) 0.0577

33)

34) A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If 40 different applicants are randomly selected, find the probability that their mean is above 215.

A) 0.3821 B) 0.1179 C) 0.4713 D) 0.0287

34)

Use the normal distribution to approximate the desired probability.

35) A coin is tossed 20 times. A person, who claims to have extrasensory perception, is asked to predict the outcome of each flip in advance. She predicts correctly on 14 tosses. What is the probability of being correct 14 or more times by guessing? Does this probability seem to verify her claim?

A) 0.0582, yes B) 0.0582, no C) 0.4418, yes D) 0.4418, no

35)

36) Find the probability that in 200 tosses of a fair die, we will obtain at least 40 fives.

A) 0.0871 B) 0.3871 C) 0.1210 D) 0.2229

36)

37) Find the probability that in 200 tosses of a fair die, we will obtain at most 30 fives.

A) 0.3229 B) 0.2946 C) 0.1871 D) 0.4936

37)

38) Merta reports that 74% of its trains are on time. A check of 60 randomly selected trains shows that 38 of them arrived on time. Find the probability that among the 60 trains, 38 or fewer

arrive on time. Based on the result, does it seem plausible that the "on-time" rate of 74% could

be correct?

A) 0.0409, yes B) 0.0409, no C) 0.0316, yes D) 0.0316, no

38)

39) Find the probability that in 200 tosses of a fair die, we will obtain at exactly 30 fives.

A) 0.1871 B) 0.0871 C) 0.0619 D) 0.0429

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Find the indicated critical z value.

40) Find the critical value zα/2 that corresponds to a 91% confidence level.

A) 1.34 B) 1.70 C) 1.75 D) 1.645

40)

A) 2.70 B) 1.81 C) 1.48 D) 1.96

41)

A) 2.05 B) 2.575 C) 1.75 D) 2.33

42)

Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level. Round the margin of error to four decimal places.

43) 95% confidence; n = 380, x = 50

A) 0.0357 B) 0.0340 C) 0.0408 D) 0.0306

43)

44) In a random sample of 192 college students, 129 had part-time jobs. Find the margin of error for the 95% confidence interval used to estimate the population proportion.

A) 0.116 B) 0.0664 C) 0.0598 D) 0.00225

44)

45) 98% confidence; the sample size is 800, of which 40% are successes

A) 0.0339 B) 0.0446 C) 0.0404 D) 0.0355

45)

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.

46) n = 56, x = 30; 95% confidence

A) 0.405 < p < 0.667 B) 0.426 < p < 0.646

C) 0.425 < p < 0.647 D) 0.404 < p < 0.668

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47) n = 109, x = 65; 88% confidence

A) 0.519 < p < 0.673 B) 0.518 < p < 0.674

C) 0.522 < p < 0.670 D) 0.523 < p < 0.669

47)

Use the given data to find the minimum sample size required to estimate the population proportion.

48) Margin of error: 0.005; confidence level: 96%; p^ and q^ unknown

A) 42,018 B) 42,148 C) 42,025 D) 32,024

48)

49) Margin of error: 0.07; confidence level: 95%; from a prior study, p^ is estimated by the decimal

equivalent of 92%.

A) 51 B) 58 C) 4 D) 174

49)

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.

50) A survey of 865 voters in one state reveals that 408 favor approval of an issue before the legislature. Construct the 95% confidence interval for the true proportion of all voters in the state who favor approval.

A) 0.438 < p < 0.505 B) 0.471 < p < 0.472

C) 0.435 < p < 0.508 D) 0.444 < p < 0.500

50)

Margin of error:

CI:

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51) Of 346 items tested, 12 are found to be defective. Construct the 98% confidence interval for the proportion of all such items that are defective.

A) 0.0118 < p < 0.0576 B) 0.0345 < p < 0.0349

C) 0.0110 < p < 0.0584 D) 0.0154 < p < 0.0540

51)

Margin of error:

CI:

Interpretation:

52) When 328 college students are randomly selected and surveyed, it is found that 122 own a car. Find a 99% confidence interval for the true proportion of all college students who own a car.

A) 0.320 < p < 0.424 B) 0.303 < p < 0.441

C) 0.328 < p < 0.416 D) 0.310 < p < 0.434

52)

Margin of error:

CI:

Interpretation:

53) Of 260 employees selected randomly from one company, 18.46% of them commute by

carpooling. Construct a 90% confidence interval for the true percentage of all employees of the company who carpool.

A) 14.5% < p < 22.4% B) 12.3% < p < 24.7%

C) 12.9% < p < 24.1% D) 13.7% < p < 23.2%

53)

Margin of error:

CI:

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54) Of 150 adults selected randomly from one town, 30 of them smoke. Construct a 99% confidence interval for the true percentage of all adults in the town that smoke.

A) 13.6% < p < 26.4% B) 14.6% < p < 25.4%

C) 12.4% < p < 27.6% D) 11.6% < p < 28.4%

54)

Margin of error:

CI:

Interpretation:

Solve the problem.

55) In a certain population, body weights are normally distributed with a mean of 152 pounds and a standard deviation of 26 pounds. How many people must be surveyed if we want to

estimate the percentage who weigh more than 180 pounds? Assume that we want 96% confidence that the error is no more than 4 percentage points.

A) 232 B) 501 C) 658 D) 317

55)

Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. Assume that the population has a normal distribution.

56) n = 10, x = 8.1, s = 4.8, 95% confidence

A) 4.67 < μ < 11.53 B) 5.32 < μ < 10.88 C) 4.72 < μ < 11.48 D) 4.68 < μ < 11.52

56)

57) n = 30, x = 84.6, s = 10.5, 90% confidence

A) 79.32 < μ < 89.88 B) 81.36 < μ < 87.84

C) 81.34 < μ < 87.86 D) 80.68 < μ < 88.52

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58) Thirty randomly selected students took the calculus final. If the sample mean was 95 and the standard deviation was 6.6, construct a 99% confidence interval for the mean score of all students.

A) 92.95 < μ < 97.05 B) 91.69 < μ < 98.31

C) 92.03 < μ < 97.97 D) 91.68 < μ < 98.32

58)

Margin of error:

CI:

Interpretation:

59) A savings and loan association needs information concerning the checking account balances of its local customers. A random sample of 14 accounts was checked and yielded a mean balance of $664.14 and a standard deviation of $297.29. Find a 98% confidence interval for the true mean checking account balance for local customers.

A) $453.59 < μ < $874.69 B) $492.52 < μ < $835.76

C) $493.71 < μ < $834.57 D) $455.65 < μ < $872.63

59)

Margin of error:

CI:

Interpretation:

Use the given information to find the minimum sample size required to estimate an unknown population mean μ. 60) Margin of error: $140, confidence level: 95%, σ = $574

A) 91 B) 45 C) 65 D) 57

60)

61) How many women must be randomly selected to estimate the mean weight of women in one age group. We want 90% confidence that the sample mean is within 3.4 lb of the population mean, and the population standard deviation is known to be 25 lb.

A) 148 B) 147 C) 145 D) 208

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Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. Assume that the population has a normal distribution.

62) The amounts (in ounces) of juice in eight randomly selected juice bottles are: 15.4 15.8 15.4 15.1

15.8 15.9 15.8 15.7

Construct a 98% confidence interval for the mean amount of juice in all such bottles.

A) 15.89 oz < μ < 15.33 oz B) 15.99 oz < μ < 15.23 oz

C) 15.23 oz < μ < 15.99 oz D) 15.33 oz < μ < 15.89 oz

62)

Margin of error:

CI:

Interpretation:

63) The football coach randomly selected ten players and timed how long each player took to perform a certain drill. The times (in minutes) were:

7.0 10.8 9.5 8.0 11.5 7.5 6.4 11.3 10.2 12.6

Determine a 95% confidence interval for the mean time for all players.

A) 8.03 min < μ < 10.93 min B) 11.03 min < μ < 7.93 min

C) 7.93 min < μ < 11.03 min D) 10.93 min < μ < 8.03 min

63)

Margin of error:

CI:

Interpretation:

Solve the problem.

64) Find the critical value χ2_R corresponding to a sample size of 19 and a confidence level of 99

percent.

A) 34.805 B) 7.015 C) 37.156 D) 6.265

64)

65) Find the chi-square value χ2_L corresponding to a sample size of 4 and a confidence level of 98

percent.

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Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation σ. Assume that the population has a normal distribution. Round the confidence interval limits to the same number of decimal places as the sample standard deviation.

66) Weights of men: 90% confidence; n = 14, x = 161.5 lb, s = 13.7 lb

A) 10.2 lb < σ < 19.3 lb B) 11.1 lb < σ < 2.7 lb

C) 10.4 lb < σ < 20.3 lb D) 10.8 lb < σ < 17.7 lb

66)

67) College students' annual earnings: 98% confidence; n = 9, x = $3361, s = $865

A) $526 < σ < $1693 B) $584 < σ < $1657

C) $681 < σ < $1128 D) $546 < σ < $1907

67)

68) The mean replacement time for a random sample of 20 washing machines is 10.9 years and the standard deviation is 2.7 years. Construct a 99% confidence interval for the standard

deviation, σ, of the replacement times of all washing machines of this type.

A) 1.8 yr < σ < 5.1 yr B) 1.9 yr < σ < 4.5 yr

C) 1.9 yr < σ < 5.7 yr D) 2.0 yr < σ < 4.3 yr

68)

CI:

Interpretation:

69) A sociologist develops a test to measure attitudes about public transportation, and 27 randomly selected subjects are given the test. Their mean score is 76.2 and their standard deviation is 21.4. Construct the 95% confidence interval for the standard deviation, σ, of the scores of all subjects.

A) 17.5 < σ < 27.8 B) 17.2 < σ < 27.2 C) 16.9 < σ < 29.3 D) 16.6 < σ < 28.6

69)

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Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation σ. Assume that the population has a normal distribution. Round the confidence interval limits to one more decimal place than is used for the original set of data.

70) The football coach randomly selected ten players and timed how long each player took to perform a certain drill. The times (in minutes) were:

9 7 15 6 15 12 8 6 14 5

Find a 95% confidence interval for the population standard deviation σ.

A) 0.8 min < σ < 2.4 min B) 2.7 min < σ < 6.6 min

C) 2.7 min < σ < 7.2 min D) 2.6 min < σ < 6.6 min

70)

CI:

Interpretation:

71) The amounts (in ounces) of juice in eight randomly selected juice bottles are: 15.2 15.1 15.9 15.5

15.6 15.1 15.8 15.0

A) 0.21 oz < σ < 0.82 oz B) 0.21 oz < σ < 0.71 oz

C) 0.22 oz < σ < 0.86 oz D) 0.20 oz < σ < 0.71 oz

71)

CI:

Interpretation:

72) The daily intakes of milk (in ounces) for ten randomly selected people were: 23.3 28.4 10.5 16.4 26.4

18.1 20.4 17.3 27.4 13.2

A) 3.78 oz < σ < 12.53 oz B) 0.88 oz < σ < 3.38 oz

C) 3.78 oz < σ < 13.95 oz D) 3.66 oz < σ < 12.53 oz

72)

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Answer Key

Testname: CHAPTERS 6&7

1) D 2) D 3) D 4) B 5) C 6) D 7) C 8) D 9) B 10) B 11) C 12) A 13) A 14) A 15) C 16) B 17) D 18) B 19) A 20) B 21) C 22) B 23) A 24) A 25) C 26) B 27) C 28) D 29) C 30) A 31) C 32) D 33) D 34) D 35) B 36) C 37) B 38) B 39) C 40) B 41) B 42) D 43) B 44) B 45) C 46) A

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Answer Key

Testname: CHAPTERS 6&7

49) B 50) A 51) A 52) B 53) A 54) D 55) C 56) A 57) C 58) D 59) A 60) C 61) B 62) D 63) A 64) C 65) D 66) C 67) D 68) B 69) C 70) C 71) A 72) C