# MATHEMATICS

14) According to the empirical rule, if the data form a “bell-shaped” normal distribution, ________ percent of the observations will be contained within 1 standard deviation around the arithmetic mean.

A) 68.26

B) 75.00

C) 88.89

D) 93.75

Answer: A

15) According to the Chebyshev rule, at least 93.75% of all observations in any data set are contained within a distance of how many standard deviations around the mean?

A) 1

B) 2

C) 3

D) 4

Answer: D

16) True or False: If the data set is approximately bell-shaped, the empirical rule will more accurately reflect the greater concentration of data close to the mean as compared to the Chebyshev rule.

Answer: TRUE

17) If two events are mutually exclusive, what is the probability that one or the other occurs?

A) 0

B) 0.50

C) 1.00

D) cannot be determined from the information given

18) If two equally likely events *A* and *B* are mutually exclusive and collectively exhaustive, what is the probability that event *A* occurs?

A) 0.

B) 0.50

C) 1.00

D) cannot be determined from the information given

Answer: B

19) If two equally likely events *A* and *B* are collectively exhaustive, what is the probability that event *A* occurs?

A) 0

B) 0.50

C) 1.00

D) cannot be determined from the information given

Answer: D

20) All the events in the sample space that are not part of the specified event are called

A) simple events.

B) joint events.

C) the sample space.

D) the complement of the event.

Answer: D

21) The employees of a company were surveyed on questions regarding their educational background (college degree or no college degree) and marital status (single or married). Of the 600 employees, 400 had college degrees, 100 were single, and 60 were single college graduates. The probability that an employee of the company does not have a college degree is ________.

A) 0.10

B) 0.33

C) 0.67

D) 0.75

Answer: B

22) 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 both house sales and interest rates will increase during the next 6 months is ________.

A) 0.10

B) 0.185

C) 0.705

D) 0.90

Answer: A

B:Sales not increase .75

C:Interest rates up .74

D:Interest rates not up .26

A or C .89

P(A and C) = P(A) + P(C) – P(A or C) = 0.25+0.74-0.89 = 0.1

A:Sales increase | B:Sales not increase | ||

C:Interest rates up | X | 74 | |

D:Interest rates not up | 26 | ||

25 | 75 | 100 |

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