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Statistics For Management And Economics 9th Edition Gerald Keller, Kenneth C Louden - Solutions

An Internet pharmacy advertises that it will deliver the over-the-counter products that customers purchase in 3 to 6 days. The manager of the company wanted to be more precise in its advertising. Accordingly, she recorded the number of days it took to deliver to customers. From the data, the
Refer to Exercise 7.14. Find the following probabilities.a. No headsb. One headc. Two headsd. At least one head LO-1
Draw a probability tree to describe the flipping of three fair coins. LO-1
Refer to Exercise 7.16. Find the following probabilities.a. Two headsb. One headc. At least one headd. At least two heads LO-1
The random variable X has the following distribution.x 2 5 7 8 P (x) .59 .15 .25 .01a. Find the mean and variance for the probability distribution below.b. Determine the probability distribution of Y where Y 5X.c. Use the probability distribution in part (b) to compute the mean and variance of
We are given the following probability distribution.x 0 1 2 3 P (x) .4 .3 .2 .1a. Calculate the mean, variance, and standard deviation.b. Suppose that Y 3X 2. For each value of X, determine the value of Y. What is the probability distribution of Y?c. Calculate the mean, variance, and standard
The number of pizzas delivered to university students each month is a random variable with the following probability distribution.x 0 1 2 3 P (X) .1 .3 .4 .2a. Find the probability that a student has received delivery of two or more pizzas this month.b. Determine the mean and variance of the number
After watching a number of children playing games at a video arcade, a statistics practitioner estimated the following probability distribution of X, the number of games per visit.x 1 2 3 4 5 6 7 P (x) .05 .15 .15 .25 .20 .10 .10a. What is the probability that a child will play more than four
Refer to Exercise 7.22.a. Determine the probability distribution of the amount of money the arcade takes in per child.b. Use the probability distribution to calculate the mean and variance of the amount of money the arcade takes in.c. Compare the answers in part (b) with those of Exercise 7.24. Are
A survey of Amazon.com shoppers reveals the following probability distribution of the number of books purchased per hit.x 0 1 2 3 4 5 6 7 P (x) .35 .25 .20 .08 .06 .03 .02 .01a. What is the probability that an Amazon.com visitor will buy four books?b. What is the probability that an Amazon.com
A university librarian produced the following probability distribution of the number of times a student walks into the library over the period of a semester.x 0 5 10 15 20 25 30 40 50 75 100 P (x) .22 .29 .12 .09 .08 .05 .04 .04 .03 .03 .01 Find the following probabilities.a.b. P(X 60)c. P(X
After analyzing the frequency with which crosscountry skiers participate in their sport, a sportswriter created the following probability distribution for X number of times per year cross-country skiers ski.x 0 1 2 3 4 5 6 7 8 P (x) .04 .09 .19 .21 .16 .12 .08 .06 .05 Find the following.a.
The natural remedy echinacea is reputed to boost the immune system, which will reduce the number P(5 … X … 7)P(X Ú 5)P(X Ú 20)of flu and colds. A 6-month study was undertaken to determine whether the remedy works. From this study, the following probability distribution of the number of
A shopping mall estimates the probability distribution of the number of stores mall customers actually enter, as shown in the table.x 0 1 2 3 4 5 6 P (x) .04 .19 .22 .28 .12 .09 .06 Find the mean and standard deviation of the number of stores entered.
When parking a car in a downtown parking lot, drivers pay according to the number of hours or parts thereof. The probability distribution of the number of hours cars are parked has been estimated as follows.x 1 2 3 4 5 6 7 8 P (x) .24 .18 .13 .10 .07 .04 .04 .20 Find the mean and standard deviation
Refer to Exercise 7.32. The cost of parking is $2.50 per hour. Calculate the mean and standard deviation of the amount of revenue each car generates. LO-1
The manager of a bookstore recorded the number of customers who arrive at a checkout counter every 5 minutes from which the following distribution was calculated. Calculate the mean and standard deviation of the random variable.x 0 1 2 3 4 P (x) .10 .20 .25 .25 .20
It cost one dollar to buy a lottery ticket, which has five prizes. The prizes and the probability that a player wins the prize are listed here. Calculate the expected value of the payoff.Prize ($) 1 million 200,000 50,000 Probability 1/10 million 1/1 million 1/500,000 Prize ($) 10,000 1,000
After an analysis of incoming faxes the manager of an accounting firm determined the probability distribution of the number of pages per facsimile as follows:x 1 2 3 4 5 6 7 P (x) .05 .12 .20 .30 .15 .10 .08 Compute the mean and variance of the number of pages per fax.
To examine the effectiveness of its four annual advertising promotions, a mail-order company has sent a questionnaire to each of its customers, asking how many of the previous year’s promotions prompted orders that would not otherwise have been made.The table lists the probabilities that were
The following table lists the bivariate distribution of X and Y.x y 1 2 1 .5 .1 2 .1 .3a. Find the marginal probability distribution of X.b. Find the marginal probability distribution of Y.c. Compute the mean and variance of X.d. Compute the mean and variance of Y.
Refer to Exercise 7.43. Compute the covariance and the coefficient of correlation. LO-1
Refer to Exercise 7.43. Use the laws of expected value and variance of the sum of two variables to compute the mean and variance of X Y. LO-1
Refer to Exercise 7.43.a. Determine the distribution of X Y.b. Determine the mean and variance of X Y.c. Does your answer to part (b) equal the answer to Exercise 7.45? LO-1
The bivariate distribution of X and Y is described here.x y 1 2 1 .28 .42 2 .12 .18a. Find the marginal probability distribution of X.b. Find the marginal probability distribution of Y.c. Compute the mean and variance of X.d. Compute the mean and variance of Y.
Refer to Exercise 7.47. Compute the covariance and the coefficient of correlation. LO-1
Refer to Exercise 7.47. Use the laws of expected value and variance of the sum of two variables to compute the mean and variance of X Y. LO-1
Refer to Exercise 7.47.a. Determine the distribution of X Y.b. Determine the mean and variance of X Y.c. Does your answer to part (b) equal the answer to Exercise 7.49? LO-1
The joint probability distribution of X and Y is shown in the following table.x y 1 2 3 1 .42 .12 .06 2 .28 .08 .04a. Determine the marginal distributions of X and Y.b. Compute the covariance and coefficient of correlation between X and Y.c. Develop the probability distribution of X Y.
The following distributions of X and of Y have been developed. If X and Y are independent, determine the joint probability distribution of X and Y.x 0 1 2 y 1 2 p(x) .6 .3 .1 p(y) .7 .3
The distributions of X and of Y are described here.If X and Y are independent, determine the joint probability distribution of X and Y.x 0 1 y 1 2 3 P (x) .2 .8 P (y) .2 .4 .4
After analyzing several months of sales data, the owner of an appliance store produced the following joint probability distribution of the number of refrigerators and stoves sold daily.Refrigerators Stoves 0 1 2 0 .08 .14 .12 1 .09 .17 .13 2 .05 .18 .04a. Find the marginal probability distribution
Canadians who visit the United States often buy liquor and cigarettes, which are much cheaper in the United States. However, there are limitations.Canadians visiting in the United States for more than 2 days are allowed to bring into Canada one bottle of liquor and one carton of cigarettes. A
There are four activities along the critical path for a project. The expected values and variances of the completion times of the activities are listed here. Determine the expected value and variance of the completion time of the project.Expected Completion Activity Time (Days) Variance 1 18 8 2 12
The operations manager of a large plant wishes to overhaul a machine. After conducting a PERT/CPM analysis he has developed the following critical path.1. Disassemble machine 2. Determine parts that need replacing 3. Find needed parts in inventory 4. Reassemble machine 5. Test machine He has
In preparing to launch a new product, a marketing manager has determined the critical path for her department. The activities and the mean and variance of the completion time for each activity along the critical path are shown in the accompanying table. Determine the mean and variance of the
A professor of business statistics is about to begin work on a new research project.Because his time is quite limited, he has developed a PERT/CPM critical path, which consists of the following activities:1. Conduct a search for relevant research articles.2. Write a proposal for a research grant.3.
Describe what happens to the expected value and standard deviation of the portfolio returns when the coefficient of correlation decreases. LO-1
A portfolio is composed of two stocks. The proportion of each stock, their expected values, and standard deviations are listed next.Stock 1 2 Proportion of portfolio .30 .70 Mean .12 .25 Standard deviation .02 .15 For each of the following coefficients of correlation calculate the expected value
An investor is given the following information about the returns on two stocks.Stock 1 2 Mean .09 .13 Standard deviation .15 .21a. If he is most interested in maximizing his returns, which stock should he choose?b. If he is most interested in minimizing his risk, which stock should he choose?
Refer to Exercise 7.63. Compute the expected value and standard deviation of the portfolio composed of 60% stock 1 and 40% stock 2. The coefficient of correlation is .4. LO-1
Refer to Exercise 7.63. Compute the expected value and standard deviation of the portfolio composed of 30% stock 1 and 70% stock 2.The following exercises require the use of a computer.Xr07-66 The monthly returns for the following stocks on the New York Stock Exchange were recorded.AT&T, Aetna,
a. Calculate the mean and variance of the monthly return for each stock.b. Determine the variance–covariance matrix. LO-1
Select the two stocks with the largest means and construct a portfolio consisting of equal amounts of both. Determine the expected value and standard deviation of the portfolio. LO-1
Select the two stocks with the smallest variances and construct a portfolio consisting of equal amounts of both. Determine the expected value and standard deviation of the portfolio. LO-1
Describe the results of Exercises 7.66 to 7.68. LO-1
An investor wants to develop a portfolio composed of shares of AT&T, Coca-Cola, Ford, and Disney.Calculate the expected value and standard deviation of the returns for a portfolio with equal proportions of all three stocks. LO-1
Suppose you want a portfolio composed of AT&T, Cigna, Disney, and Ford. Find the expected value and standard deviation of the returns for the following portfolio.AT&T 30%Cigna 20%Disney 40%Ford 10% LO-1
Repeat Exercise 7.71 using the following proportions.Compare your results with those of Exercise 7.71.AT&T 30%Cigna 10%Disney 40%Ford 20% LO-1
a. Calculate the mean and variance of the monthly return for each stock.b. Determine the correlation matrix. LO-1
Select the two stocks with the largest means and construct a portfolio consisting of equal amounts of both. Determine the expected value and standard deviation of the portfolio. LO-1
Select the two stocks with the smallest variances and construct a portfolio consisting of equal amounts of both. Determine the expected value and standard deviation of the portfolio. LO-1
Describe the results of Exercises 7.73 to 7.75. LO-1
An investor wants to develop a portfolio composed of shares of Bank of Montreal, Enbridge, and Fortis.Calculate the expected value and standard deviation of the returns for a portfolio with the following proportions.Bank of Montreal 20%Enbridge 30%Fortis 50%
Suppose you want a portfolio composed of Barrick Gold, Bell Canada Enterprises, Telus, and Trans-Canada Ltd. Find the expected value and standard deviation of the returns for the following portfolio.Barrick Gold 50%Bell Canada Enterprises 25%Telus 15%TransCanada 10%
Repeat Exercise 7.78 using the following proportions.Compare your results with those of Exercise 7.78.Barrick Gold 20%Bell Canada Enterprises 40%Telus 20%TransCanada 20%
a. Calculate the mean and variance of the monthly return for each stock.b. Determine which four stocks you would include in your portfolio if you wanted a large expected value.c. Determine which four stocks you would include in your portfolio if you wanted a small variance.
Suppose you want a portfolio composed of Cisco Systems, Intel, Microsoft, and Research in Motion.Find the expected value and standard deviation of the returns for the following portfolio.Cisco Systems 30%Intel 15%Microsoft 25%Research in Motion 30%
An investor wants to acquire a portfolio composed of Cisco Systems, Intel, Microsoft, and Research in Motion. Moreover, he wants the expected value to be at least 1%. Try several sets of proportions(remember, they must add to 1.0) to see if you can find the portfolio with the smallest variance.
Refer to Exercise 7.81.a. Compute the expected value and variance of the portfolio described next.Cisco Systems 26.59%Intel 2.49%Microsoft 54.74%Research in Motion 16.19%b. Can you do better? In other words, can you find a portfolio whose expected value is greater than or equal to 1% and whose
Repeat Exercise 7.84 using Table 1 in Appendix B.
Repeat Exercise 7.84 using Excel or Minitab.
Repeat Exercise 7.87 using Table 1 in Appendix B.
Repeat Exercise 7.87 using Excel or Minitab.
Suppose X is a binomial random variable with n 25 and p .7. Use Table 1 to find the following.a. P(X 18)b. P(X 15)c.d.
Repeat Exercise 7.90 using Excel or Minitab.
In the United States, voters who are neither Democrat nor Republican are called Independents. It is believed that 10% of all voters are Independents.A survey asked 25 people to identify themselves as Democrat, Republican, or Independent.a. What is the probability that none of the people are
The probability of winning a game of craps (a dicethrowing game played in casinos) is 244/495.a. What is the probability of winning 5 or more times in 10 games?b. What is the expected number of wins in 100 games?
In 2000, Northwest Airlines boasted that 77.4% of its flights were on time. If we select five Northwest flights at random, what is the probability that all five are on time? (Source: Department of Transportation.)
The number of magazine subscriptions per household is represented by the following probability distribution.Magazine subscriptions per household 0 1 2 3 4 Probability .48 .35 .08 .05 .04a. Calculate the mean number of magazine subscriptions per household.b. Find the standard deviation.
The distribution of the number of home runs in soft-ball games is shown here.Number of home runs 0 1 2 3 4 5 Probability .05 .16 .41 .27 .07 .04a. Calculate the mean number of home runs.b. Find the standard deviation.
Advertising researchers have developed a theory that states that commercials that appear in violent television shows are less likely to be remembered and will thus be less effective. After examining samples of viewers who watch violent and nonviolent programs and asking them a series of five
Xr03-05 The number of items rejected daily by a manufacturer because of defects was recorded for the past 30 days. The results are as follows.4 9 13 7 5 8 12 15 5 7 3 8 15 17 19 6 4 10 8 22 16 9 5 3 9 19 14 13 18 7a. Construct a histogram.b. Construct an ogive.c. Describe the shape of the histogram.
Xr03-06 The final exam in a third-year organizational behavior course requires students to write several essay-style answers. The numbers of pages for a sample of 25 exams were recorded. These data are shown here.5 8 9 3 12 8 5 7 3 8 9 5 2 7 12 9 6 3 8 7 10 9 12 7 3a. Draw a histogram.b. Draw an
Xr03-07 A large investment firm on Wall Street wants to review the distribution of ages of its stockbrokers.The firm believes that this information can be useful in developing plans to recruit new brokers. The ages of a sample of 40 brokers are shown here.46 28 51 34 29 40 38 33 41 52 53 40 50 33
Xr03-08 The numbers of weekly sales calls by a sample of 30 telemarketers are listed here. Draw a histogram of these data and describe it.14 8 6 12 21 4 9 3 25 17 9 5 8 18 16 3 17 19 10 15 5 20 17 14 19 7 10 15 10 8
Xr03-09 The amount of time (in seconds) needed to complete a critical task on an assembly line was measured for a sample of 50 assemblies. These data are as follows:30.3 34.5 31.1 30.9 33.7 31.9 33.1 31.1 30.0 32.7 34.4 30.1 34.6 31.6 32.4 32.8 31.0 30.2 30.2 32.8 31.1 30.7 33.1 34.4 31.0 32.2 30.9
Xr03-10 A survey of individuals in a mall asked 60 people how many stores they will enter during this visit to the mall. The responses are listed here.3 2 4 3 3 9 2 4 3 6 2 2 8 7 6 4 5 1 5 2 3 1 1 7 3 4 1 1 4 8 0 2 5 4 4 4 6 2 2 5 3 8 4 3 1 6 9 1 4 4 1 0 4 6 5 5 5 1 4 3a. Draw a histogram.b. Draw
Xr03-11 A survey asked 50 baseball fans to report the number of games they attended last year. The results are listed here. Use an appropriate graphical technique to present these data and describe what you have learned.5 15 14 7 8 16 26 6 15 23 11 15 6 4 7 8 19 16 9 9 8 7 10 5 8 8 6 6 21 10 5 24 5
Xr03-12 To help determine the need for more golf courses, a survey was undertaken. A sample of 75 self-declared golfers was asked how many rounds of golf they played last year. These data are as follows:18 26 16 35 30 15 18 15 18 29 25 30 35 14 20 18 24 21 25 18 29 23 15 19 27 28 9 17 28 25 23 20
Xr03-13 The annual incomes for a sample of 200 firstyear accountants were recorded. Summarize these data using a graphical method. Describe your results.
Xr03-14 The real estate board in a suburb of Los Angeles wanted to investigate the distribution of the prices (in $ thousands) of homes sold during the past year.a Draw a histogram.b. Draw an ogive.c. Draw a stem-and-leaf display (if your software allows it).d. Describe what you have learned.
Xr03-15 The number of customers entering a bank in the first hour of operation for each of the last 200 days was recorded. Use a graphical technique to extract information. Describe your findings.
Xr03-16 The lengths of time (in minutes) to serve 420 customers at a local restaurant were recorded.a. How many bins should a histogram of these data contain?b. Draw a histogram using the number of bins specified in part (a).c. Is the histogram symmetric or skewed?d. Is the histogram bell shaped?
Xr03-17 The marks of 320 students on an economics midterm test were recorded. Use a graphical technique to summarize these data. What does the graph tell you?
Xr03-18 The lengths (in inches) of 150 newborn babies were recorded. Use whichever graphical technique you judge suitable to describe these data.What have you learned from the graph?
Xr03-19 The number of copies made by an office copier was recorded for each of the past 75 days.Graph the data using a suitable technique.Describe what the graph tells you.
Xr03-20 Each of a sample of 240 tomatoes grown with a new type of fertilizer was weighed (in ounces) and recorded. Draw a histogram and describe your findings.
Xr03-21 The volume of water used by each of a sample of 350 households was measured (in gallons)and recorded. Use a suitable graphical statistical method to summarize the data. What does the graph tell you?
Xr03-22 The number of books shipped out daily by Amazon.com was recorded for 100 days. Draw a histogram and describe your findings.
Xr03-23 A small bank that had not yet used a scorecard wanted to determine whether a scorecard would be advantageous. The bank manager took a random sample of 300 loans that were granted and scored each on a scorecard borrowed from a similar bank. This scorecard is based on the responses supplied
Xr03-24 Refer to Exercise 3.23. The bank decided to try another scorecard, this one based not on the responses of the applicants but on credit bureau reports, which list problems such as late payments and previous defaults. The scores using the new scorecard of those who repaid and the scores of
The GSS asked respondents to specify their highest year of school completed (EDUC).a. Is this type of data interval, ordinal, or nominal?b. GSS2008* Use a graphical technique to present these data for the 2008 survey.c. Briefly describe your results.
GSS2008* Graphically display the results of the GSS 2008 question, On average days how many hours do you spend watching television (TVHOURS)?Briefly describe what you have discovered.
GSS2008* Employ a graphical technique to present the ages (AGE) of the respondents in the 2008 survey.Describe your results.
GSS2008* The survey in 2008 asked “If working, fullor part-time, how many hours did you work last week at all jobs (HRS)?” Summarize these data with a graphical technique.
We recorded the monthly average retail price of gasoline (in cents per gallon) since January 1976. Some of these data are displayed below. Draw a line chart to describe these data and briefly describe the results.Year Month Price per gallon 1976 1 60.5 1976 2 60.0 1976 3 59.4 1976 4 59.2 1976 5
Xr03-29 The fees television broadcasters pay to cover the summer Olympic Games has become the largest source of revenue for the host country. Below we list the year, city, and revenue in millions of U.S. dollars paid by television broadcasters around the world.Draw a chart to describe these prices
Xr03-30 The number of females enlisted in the United States Army from 1971 to 2007 are listed here. Draw a line chart, and describe what the chart tells you.Females Females Year enlisted Year enlisted 1971 11.8 1990 71.2 1972 12.3 1991 67.8 1973 16.5 1992 61.7 1974 26.3 1993 60.2 1975 37.7 1994
Xr03-31 The United States spends more money on health care than any other country. To gauge how fast costs are increasing, the following table was produced, listing the total health-care expenditures in the United States annually for 1981 to 2006 (costs are in $billions).a. Graphically present

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