# MATHEMATICS

23) The probability that house sales will increase in the next 6 months is estimated to be 0.25. The probability that the interest rates on housing loans will go up in the same period is estimated to be 0.74. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89. The probability that neither house sales nor interest rates will increase during the next 6 months is ________.

A) 0.11

B) 0.195

C) 0.89

D) 0.90

Answer: A

24) Which of the following about the binomial distribution is NOT a true statement?

A) The probability of the event of interest must be constant from trial to trial.

B) Each outcome is independent of the other.

C) Each outcome may be classified as either “event of interest” or “not event of interest.”

D) The random variable of interest is continuous.

Answer: D

25) A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab conducts. Suppose the mean cost of rats used in lab experiments turned out to be $13.00 per week. Interpret this value.

A) Most of the weeks resulted in rat costs of $13.00.

B) The median cost for the distribution of rat costs is $13.00.

C) The expected or average cost for all weekly rat purchases is $13.00.

D) The rat cost that occurs more often than any other is $13.00.

Answer: C

26) Which of the following about the normal distribution is NOT true?

A) Theoretically, the mean, median, and mode are the same.

B) About 2/3 of the observations fall within ±1 standard deviation from the mean.

C) It is a discrete probability distribution.

D) Its parameters are the mean, *μ*, and standard deviation, *σ*.

Answer: C

27) The value of the cumulative standardized normal distribution at *Z *is 0.8770. The value of *Z *is ________.

A) 0.18

B) 0.81

C) 1.16

D) 1.47

Answer: C

28) For some value of *Z*, the value of the cumulative standardized normal distribution is 0.8340. The value of *Z* is ________.

A) 0.07

B) 0.37

C) 0.97

D) 1.06

Answer: C

29) A company that sells annuities must base the annual payout on the probability distribution of the length of life of the participants in the plan. Suppose the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 3.5 years. Find the age at which payments have ceased for approximately 86% of the plan participants.

Answer: 71.78 years old

30) If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, 75.8% of the college students will take more than how many minutes when trying to find a parking spot in the library parking lot?

A) 2.8 minutes

B) 3.2 minutes

C) 3.4 minutes

D) 4.2 minutes

Answer: A

31) The owner of a fish market determined that the average weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound. Assuming the weights of catfish are normally distributed, above what weight (in pounds) do 89.80% of the weights occur?

Answer: 2.184 pounds

32) True or False: The probability that a standard normal random variable, *Z*, is below 1.96 is 0.4750.

Answer: FALSE

33) The amount of tea leaves in a can from a particular production line is normally distributed with *μ* = 110 grams and σ = 25 grams. What is the probability that a randomly selected can will contain less than 100 grams or more than 120 grams of tea leaves?

Answer: 0.6892

34) The amount of tea leaves in a can from a particular production line is normally distributed with *μ* = 110 grams and σ = 25 grams. Approximately 83% of the can will have at least how many grams of tea leaves?

Answer: 86.15 using Excel or 86.25 using Table E.2

35) You were told that the mean score on a statistics exam is 75 with the scores normally distributed. In addition, you know the probability of a score between 55 and 60 is 4.41% and that the probability of a score greater than 90 is 6.68%. What is the probability of a score lower than 55?

Answer: 2.27% or 0.0227

36) The owner of a fish market determined that the average weight for a catfish is 3.2 pounds. He also knew that the probability of a randomly selected catfish that would weigh more than 3.8 pounds is 20% and the probability that a randomly selected catfish that would weigh less than 2.8 pounds is 30%. The probability that a randomly selected catfish will weigh between 2.6 and 3.6 pounds is ________.

Answer: 50% or 0.5

37) The owner of a fish market determined that the average weight for a catfish is 3.2 pounds. He also knew that the probability of a randomly selected catfish that would weigh more than 3.8 pounds is 20% and the probability that a randomly selected catfish that would weigh less than 2.8 pounds is 30%. The middle 40% of the catfish will weigh between ________ pounds and ________ pounds.

Answer: 2.8 and 3.6

38) Which of the following sampling methods is a probability sample?

A) convenience sample

B) quota sample

C) stratified sample

D) judgment sample

Answer: C

39) At U.S. Data Corporation’s web site, they advertised that “Because of our commitment to quality and our vast amount of industry knowledge and experience, we have grown to be one of America’s leading providers of mailing lists, marketing data, sales leads and research data. We maintain databases of information on consumers and businesses nationwide that set industry standards for mission critical currency, reliability, and accuracy.” Trying to reach 500 potential donors for their annual phone donation campaign, a local fire department purchased a list of donors from the company. This list is an example of a

A) population.

B) statistic.

C) parameter.

D) frame.

Answer: D

40) To find out the potential impact of a new zoning law on a neighborhood, the legislators conduct a focus group interview by inviting the members of the housing owners association of that neighborhood. This is an example of a

A) systematic sample.

B) simple random sample.

C) judgment sample.

D) cluster sample.

Answer: C

41) ________ results from the exclusion of certain groups of subjects from a population frame.

Answer: Coverage error

42) Coverage error results in a ________.

Answer: selection bias

43) True or False: The professor of a business statistics class wanted to find out the mean amount of time per week her students spent studying for the class. She divided the fifty students on her roster into ten groups starting from the first student on the roster. The first student was randomly selected from the first group. Then every tenth student was selected from the remaining students. This is an example of a cluster sample.

Answer: FALSE

44) True or False: The question: “Have you used any form of illicit drugs over the past two months?” will most likely result in measurement error if the question is answered.

Answer: TRUE

45) If the expected value of a sample statistic is equal to the parameter it is estimating, then we call that sample statistic

A) unbiased.

B) minimum variance.

C) biased.

D) random.

Answer: A

46) For air travelers, one of the biggest complaints is of the waiting time between when the airplane taxis away from the terminal until the flight takes off. This waiting time is known to have a right-skewed distribution with a mean of 10 minutes and a standard deviation of 8 minutes. Suppose 100 flights have been randomly sampled. Describe the sampling distribution of the mean waiting time between when the airplane taxis away from the terminal until the flight takes off for these 100 flights.

A) Distribution is right-skewed with mean = 10 minutes and standard error = 0.8 minutes.

B) Distribution is right-skewed with mean = 10 minutes and standard error = 8 minutes.

C) Distribution is approximately normal with mean = 10 minutes and standard error = 0.8 minutes.

D) Distribution is approximately normal with mean = 10 minutes and standard error = 8 minutes.

Answer: C

47) The distribution of the number of loaves of bread sold per day by a large bakery over the past five years has a mean of 7,750 and a standard deviation of 145 loaves. Suppose a random sample of *n* = 40 days has been selected. What is the approximate probability that the mean number of loaves sold in the sampled days exceeds 7,895 loaves?

Answer: approximately 0

48) Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a recent year. Suppose a sample of 100 major league players was taken. What was the standard error for the sample mean salary?

A) $0.012 million

B) $0.12 million

C) $12 million

D) $1,200.0 million

Answer: B

49) At a computer manufacturing company, the actual size of computer chips is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. A random sample of 12 computer chips is taken. What is the probability that the sample mean will be between 0.99 and 1.01 centimeters?

Answer: 0.2710 using Excel or 0.2736 using Table E.2

50) The standard error of the population proportion will become larger

A) as the population proportion approaches 0.

B) as the population proportion approaches 0.50.

C) as the population proportion approaches 1.00.

D) as the sample size increases.

Answer: B

51) The head librarian at the Library of Congress has asked her assistant for an interval estimate of the mean number of books checked out each day. The assistant provides the following interval estimate: from 740 to 920 books per day. What is an efficient, unbiased point estimate of the number of books checked out each day at the Library of Congress?

A) 740

B) 830

C) 920

D) 1,660

Answer: B

52) True or False: The difference between the lower limit of a confidence interval and the point estimate used in constructing the confidence interval is called the sampling error.

Answer: TRUE

53) True or False: The width of a confidence interval equals twice the sampling error.

Answer: TRUE

54) True or False: Given a sample mean of 2.1 and a population standard deviation of 0.7 from a sample of 10 data points, a 90% confidence interval will have a width of 2.36.

Answer: FALSE

55) It is desired to estimate the mean total compensation of CEOs in the Service industry. Data were randomly collected from 18 CEOs and the 95% confidence interval was calculated to be ($2,181,260, $5,836,180). Based on the interval above, do you believe the mean total compensation of CEOs in the Service industry is more than $3,000,000?

A) Yes, and I am 95% confident of it.

B) Yes, and I am 78% confident of it.

C) I am 95% confident that the mean compensation is $3,000,000.

D) I cannot conclude that the mean exceeds $3,000,000 at the 95% confidence level.

Answer: D