# Mathematics

Class Frequency

2 up to 4 21

4 up to 6 59

6 up to 8 81

8 up to 10 21

a.

Calculate the population mean. (Round your answer to 2 decimal places.)

Population mean

b.

Calculate the population variance and the population standard deviation. (Round your intermediate calculations to 4 decimal places and final answers to 2 decimal places.)

Population variance

Population standard deviation

rev: 07_31_2013_QC_32713

31.

Which of the following variables is not continuous?

Time of a flight between Atlanta and Chicago

Height of NBA players

The number of obtained heads when a fair coin is tossed 20 times

Average temperature in the month of July in Orlando

32.

The one-year return (in %) for 24 mutual funds is as follows:

–10.7 –1.4 0.9 6.1 –15.9 –7.5

21.5 –9.6 4.5 11.1 14.5 4.7

–8.4 –8.4 19.5 14.9 29.3 7.7

22.0 24.8 –0.4 11.1 5.0 –11.0

PictureClick here for the Excel Data File

a.

Construct a frequency distribution using classes of –20 up to –10, –10 up to 0, etc.

Class (in %) Frequency

–20 up to –10

–10 up to 0

0 up to 10

10 up to 20

20 up to 30

Total

b.

Construct the relative frequency, the cumulative frequency, and the cumulative relative frequency distributions. (Round “relative frequency” and “cumulative relative frequency” answers to 3 decimal places.)

Class (in %) Relative

Frequency Cumulative

Frequency Cumulative

Relative Frequency

–20 up to –10

–10 up to 0

0 up to 10

10 up to 20

20 up to 30

Total

c-1. How many of the funds had returns of at least 20% but less than 30%?

Number of funds

c-2. How many of the funds had returns of 0% or more?

Number of funds

d-1.

What percent of the funds had returns of at least –10% but less than 0%? (Round your answer to 1 decimal place.)

Percent of funds

d-2.

What percent of the funds had returns less than 20%? (Round your answer to 1 decimal place.)

Percent of funds

rev: 06_24_2013_QC_31991, 07_05_2013_QC_32367

©2015 McGraw-Hill Education. All rights reserved.

33.

Investment advisors recommend risk reduction through international diversification. International investing allows you to take advantage of the potential for growth in foreign economies, particularly in emerging markets. Janice Wong is considering investment in either Europe or Asia. She has studied these markets and believes that both markets will be influenced by the U.S. economy, which has a 16% chance for being good, a 57% chance for being fair, and a 27% chance for being poor. Probability distributions of the returns for these markets are given in the accompanying table.

State of the

U.S. Economy Returns

in Europe Returns

in Asia

Good 14% 28%

Fair 5% 7%

Poor −12% −10%

a.

Find the expected value and the standard deviation of returns in Europe and Asia. (Round your intermediate calculations to 4 decimal places and final answers to 2 decimal places.)

Europe Asia

Expected value % %

Standard deviation

b. What will Janice pick as an investment if she is risk neutral?

Investment in Europe

Investment in Asia

rev: 08_07_2013_QC_33420

34.

Consider the following probabilities: P(Ac) = 0.32, P(B) = 0.58, and P(A ∩ Bc) = 0.25.

a. Find P(A | Bc). (Do not round intermediate calculations. Round your answer to 2 decimal places.)

P(A | Bc)

b. Find P(Bc | A). (Do not round intermediate calculations. Round your answer to 3 decimal places.)

P(Bc | A)

c. Are A and B independent events?

Yes because P(A | Bc) = P(A).

Yes because P(A ∩ Bc) ≠ 0.

No because P(A | Bc) ≠ P(A).

No because P(A ∩ Bc) ≠ 0.

rev: 08_06_2013_QC_32707

35.

The probabilities that stock A will rise in price is 0.64 and that stock B will rise in price is 0.36. Further, if stock B rises in price, the probability that stock A will also rise in price is 0.56.

a.

What is the probability that at least one of the stocks will rise in price? (Round your answer to 2 decimal places.)

Probability

b. Are events A and B mutually exclusive?

Yes because P(A | B) = P(A).

Yes because P(A ∩ B) = 0.

No because P(A | B) ≠ P(A).

No because P(A ∩ B) ≠ 0.

c. Are events A and B independent?

Yes because P(A | B) = P(A).

Yes because P(A ∩ B) = 0.

No because P(A | B) ≠ P(A).

No because P(A ∩ B) ≠ 0.

rev: 08_06_2013_QC_32707

36.

A sample of patients arriving at Overbrook Hospital’s emergency room recorded the following body temperature readings over the weekend:

102.6 99.8 100.7 100.9 100.5 102.4 101.3 99.2 100.5 100.9

99.8 100.3 99.8 100.5 100.9 100.7 100.3 100.2 99.6 99.7

PictureClick here for the Excel Data File

a. Construct a stem-and-leaf diagram.

Stem Leaf

b. Interpret the stem-and-leaf diagram.

The distribution is Positively Skewed.

The distribution is Negatively Skewed.

The distribution is symmetric.

37.

A professor has learned that nine students in her class of 24 will cheat on the exam. She decides to focus her attention on eleven randomly chosen students during the exam.

a.

What is the probability that she finds at least one of the students cheating? (Round your intermediate calculations and final answers to 4 decimal places.)

Probability

b.

What is the probability that she finds at least one of the students cheating if she focuses on twelve randomly chosen students? (Round your intermediate calculations and final answers to 4 decimal places.)

Probability

rev: 08_07_2013_QC_33420

38.

At the end of a semester, college students evaluate their instructors by assigning them to one of the following categories: Excellent, Good, Average, Below Average, and Poor. The measurement scale is a(n) ____________.

nominal scale

ratio scale

ordinal scale

interval scale

39.

Consider the following contingency table.

B Bc

A 23 21

Ac 30 26

a.

Convert the contingency table into a joint probability table. (Round your intermediate calculations and final answers to 4 decimal places.)

B

Bc

Total

A

Ac

Total

b. What is the probability that A occurs? (Round your intermediate calculations and final answer to 4 decimal places.)

Probability

c. What is the probability that A and B occur? (Round your intermediate calculations and final answer to 4 decimal places.)

Probability

d.

Given that B has occurred, what is the probability that A occurs? (Round your intermediate calculations and final answer to 4 decimal places.)

Probability

e.

Given that Ac has occurred, what is the probability that B occurs? (Round your intermediate calculations and final answer to 4 decimal places.)

Probability

f. Are A and B mutually exclusive events?

Yes because P(A | B) ≠ P(A).

Yes because P(A ∩ B) ≠ 0.

No because P(A | B) ≠ P(A).

No because P(A ∩ B) ≠ 0.

g. Are A and B independent events?

Yes because P(A | B) ≠ P(A).

Yes because P(A ∩ B) ≠ 0.

No because P(A | B) ≠ P(A).

No because P(A ∩ B) ≠ 0.

rev: 08_06_2013_QC_32707, 11_10_2013_QC_38348

40.

Consider the following returns for two investments, A and B, over the past four years:

Investment 1: 9% 10% –7% 15%

Investment 2: 7% 9% –16% 14%

a-1.

Calculate the mean for each investment. (Round your answers to 2 decimal places.)

Mean

Investment 1 percent

Investment 2 percent

a-2.

Which investment provides the higher return?

Investment 2

Investment 1

b-1.

Calculate the standard deviation for each investment. (Round your answers to 2 decimal places.)

Standard

Deviation

Investment 1

Investment 2

b-2.

Which investment provides less risk?

Investment 1

Investment 2

c-1.

Given a risk-free rate of 1.2%, calculate the Sharpe ratio for each investment. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Sharpe Ratio

Investment 1

Investment 2

c-2. Which investment has performed better?

Investment 2

Investment 1

rev: 07_31_2013_QC_32713, 11_10_2013_QC_38348

41.

Which of the following represents a population and a sample from that population?

Freshmen at St. Joseph’s University and basketball players at St. Joseph’s University

Teachers in a high school and members of the parent teacher group

Residents of Albany, New York, and registered voters in Albany, New York

Fans at a concert who purchase t-shirts and fans at a concert who purchase soda

42.

(Use computer) Assume that X is a hypergeometric random variable with N = 54, S = 21, and n = 8. Calculate the following probabilities. (Round your answers to 4 decimal places.)

a. P(X = 6)

b. P(X ≥ 2)

c. P(X ≤ 7)

43.

Which scales of data measurement are associated with quantitative data?

Interval and ratio

Nominal and ordinal

Ratio and nominal

Ordinal and interval

44.

Which of the following is a quantitative variable?

All of the Answers

House size

House price

House age

45.

(Use computer) A committee of 39 members consists of 21 men and 18 women. A subcommittee consisting of 13 randomly selected members will be formed.

a.

What are the expected number of men and women in the subcommittee?

Expected

Number

Men

Women

b.

What is the probability that at least four of the members in the subcommittee will be women? (Round your answer to 4 decimal places.)

Probability

46.

The following relative frequency distribution was constructed from a population of 450. Calculate the population mean, the population variance, and the population standard deviation. (Round your intermediate calculations to 4 decimal places and final answers to 2 decimal places.)

Class Relative Frequency

−20 up to −10 0.10

−10 up to 0 0.22

0 up to 10 0.36

10 up to 20 0.32

Population mean

Population variance

Population standard deviation

rev: 07_31_2013_QC_32713

47.

A recent survey of 200 small firms (annual revenue less than $10 million) asked whether an increase in the minimum wage would cause the firm to decrease capital spending. Possible responses to the survey question were: “Yes,” “No,” or “Don’t Know.” These data are best classified as ____________.

ratio scale

nominal scale

interval scale

ordinal scale

48.

A manager of a local retail store analyzes the relationship between advertising and sales by reviewing the store’s data for the previous six months.

Advertising (in $100s) Sales (in $1,000s)

274 198

67 55

66 54

65 53

276 200

236 200

PictureClick here for the Excel Data File

a.

Calculate the mean of advertising and the mean of sales. (Round your answers to 2 decimal places.)

Mean

Advertising

Sales

b.

Calculate the standard deviation of advertising and the standard deviation of sales. (Round your answers to 2 decimal places.)

Standard Deviation

Advertising

Sales

c-1. Calculate the covariance between advertising and sales. (Round your answer to 2 decimal places.)

Covariance

c-2.

Interpret the covariance between advertising and sales.

No correlation

Positive correlation

Negative correlation

d-1.

Calculate the correlation coefficient between advertising and sales. (Round your answer to 2 decimal places.)

Correlation coefficient

d-2.

Interpret the correlation coefficient between advertising and sales.

Weak positive correlation

Strong negative correlation

Strong positive correlation

No correlation

Weak negative correlation

rev: 07_31_2013_QC_32713

©2015 McGraw-Hill Education. All rights reserved.

49.

(Use computer) Assume that X is a Poisson random variable with μ = 24. Calculate the following probabilities. (Round your intermediate calculations and final answers to 4 decimal places.)

a. P(X ≤ 19)

b. P(X = 21)

c. P(X > 26)

d. P(21 ≤ X ≤ 31)

rev: 08_07_2013_QC_33420

50.

Let P(A) = 0.54, P(B) = 0.25, and P(A ∩ B) = 0.22.

a. Are A and B independent events?

Yes because P(A | B) = P(A).

Yes because P(A ∩ B) ≠ 0.

No because P(A | B) ≠ P(A).

No because P(A ∩ B) ≠ 0.

b. Are A and B mutually exclusive events?

Yes because P(A | B) = P(A).

Yes because P(A ∩ B) ≠ 0.

No because P(A | B) ≠ P(A).

No because P(A ∩ B) ≠ 0.

c. What is the probability that neither A nor B takes place? (Round your answer to 2 decimal places.)

Probability

rev: 08_06_2013_QC_32707