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essentials of statistics

Essentials Of Statistics For Business And Economics 5th Edition David R. Anderson, Dennis J. Sweeney, Thomas A. Williams - Solutions

55. The budgeting process for a midwestern college resulted in expense forecasts for the coming year (in $ millions) of $9, $10, $11, $12, and $13. Because the actual expenses are unknown, the following respective probabilities are assigned: .3, .2, .25, .05, and .2.a. Show the probability
54. The American Association of Individual Investors publishes an annual guide to the top mutual funds (The Individual Investor’s Guide to the Top Mutual Funds, 22e, American Association of Individual Investors, 2003). Table 5.10 contains their ratings of the total risk for 29 categories of
53. The Barron’s Big Money Poll asked 131 investment managers across the United States about their short-term investment outlook (Barron’s, October 28, 2002). Their responses showed 4% were very bullish, 39% were bullish, 29% were neutral, 21% were bearish, and 7% were very bearish. Let x be
52. A shipment of 10 items has two defective and eight nondefective items. In the inspection of the shipment, a sample of items will be selected and tested. If a defective item is found, the shipment of 10 items will be rejected.a. If a sample of three items is selected, what is the probability
51. The 2003 Zagat Restaurant Survey provides food, decor, and service ratings for some of the top restaurants across the United States. For 15 top-ranking restaurants located in Boston, the average price of a dinner, including one drink and tip, was $48.60. You are leaving for a business trip to
50. Axline Computers manufactures personal computers at two plants, one in Texas and the other in Hawaii. The Texas plant has 40 employees; the Hawaii plant has 20. A random sample of 10 employees is to be asked to fill out a benefits questionnaire.a. What is the probability that none of the
49. Blackjack, or twenty-one as it is frequently called, is a popular gambling game played in Las Vegas casinos. A player is dealt two cards. Face cards (jacks, queens, and kings) and tens have a point value of 10. Aces have a point value of 1 or 11. A 52-card deck contains 16 cards with a point
48. In a survey conducted by the Gallup Organization, respondents were asked, “What is your favorite sport to watch?” Football and basketball ranked number one and two in terms of preference (http://www.gallup.com, January 3, 2004). Assume that in a group of 10 individuals, seven preferred
47. Suppose N 15 and r 4. What is the probability of x 3 for n 10?
46. Suppose N 10 and r 3. Compute the hypergeometric probabilities for the following values of n and x.a. n 4, x 1.b. n 2, x 2.c. n 2, x 0.d. n 4, x 2.
45. The National Safety Council (NSC) estimates that off-the-job accidents cost U.S. businesses almost $200 billion annually in lost productivity (National Safety Council, March 2006). Based on NSC estimates, companies with 50 employees are expected to average three employee off-the-job accidents
44. An average of 15 aircraft accidents occur each year (The World Almanac and Book of Facts, 2004).a. Compute the mean number of aircraft accidents per month.b. Compute the probability of no accidents during a month.c. Compute the probability of exactly one accident during a month.d. Compute the
43. Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. The mean arrival rate is 10 passengers per minute.a. Compute the probability of no arrivals in a one-minute period.b. Compute the probability that three or fewer passengers
42. More than 50 million guests stay at bed and breakfasts (B&Bs) each year. The Web site for the Bed and Breakfast Inns of North America (http://www.bestinns.net), which averages approximately seven visitors per minute, enables many B&Bs to attract guests (Time, September 2001).a. Compute the
41. During the period of time that a local university takes phone-in registrations, calls come in at the rate of one every two minutes.a. What is the expected number of calls in one hour?b. What is the probability of three calls in five minutes?c. What is the probability of no calls in a
40. Phone calls arrive at the rate of 48 per hour at the reservation desk for Regional Airways.a. Compute the probability of receiving three calls in a 5-minute interval of time.b. Compute the probability of receiving exactly 10 calls in 15 minutes.c. Suppose no calls are currently on hold. If the
39. Consider a Poisson distribution with a mean of two occurrences per time period.a. Write the appropriate Poisson probability function.b. What is the expected number of occurrences in three time periods?c. Write the appropriate Poisson probability function to determine the probability of x
38. Consider a Poisson distribution with μ 3.a. Write the appropriate Poisson probability function.b. Compute f(2).c. Compute f(1).d. Compute P(x 2).
37. Twenty-three percent of automobiles are not covered by insurance (CNN, February 23, 2006). On a particular weekend, 35 automobiles are involved in traffic accidents.a. What is the expected number of these automobiles that are not covered by insurance?b. What is the variance and standard
36. According to a survey conducted by TD Ameritrade, one out of four investors have exchange-traded funds in their portfolios (USA Today, January 11, 2007). For a sample of 20 investors, answer the following questions:a. Compute the probability that exactly four investors have exchange-traded
35. A university found that 20% of its students withdraw without completing the introductory statistics course. Assume that 20 students registered for the course.a. Compute the probability that two or fewer will withdraw.b. Compute the probability that exactly four will withdraw.c. Compute the
34. The Census Bureau’s Current Population Survey shows 28% of individuals, ages 25 and older, have completed four years of college (The New York Times Almanac, 2006). For a sample of 15 individuals, ages 25 and older, answer the following questions:a. What is the probability four will have
33. Fifty percent of Americans believed the country was in a recession, even though technically the economy had not shown two straight quarters of negative growth (BusinessWeek, July 30, 2001). For a sample of 20 Americans, make the following calculations.a. Compute the probability that exactly 12
32. Military radar and missile detection systems are designed to warn a country of an enemy attack. A reliability question is whether a detection system will be able to identify an attack and issue a warning. Assume that a particular detection system has a .90 probability of detecting a missile
31. Nine percent of undergraduate students carry credit card balances greater than $7000(Reader’s Digest, July 2002). Suppose 10 undergraduate students are selected randomly to be interviewed about credit card usage.a. Is the selection of 10 students a binomial experiment? Explain.b. What is the
30. When a new machine is functioning properly, only 3% of the items produced are defective. Assume that we will randomly select two parts produced on the machine and that we are interested in the number of defective parts found.a. Describe the conditions under which this situation would be a
29. In San Francisco, 30% of workers take public transportation daily (USA Today, December 21, 2005).a. In a sample of 10 workers, what is the probability that exactly three workers take public transportation daily?b. In a sample of 10 workers, what is the probability that at least three workers
28. AHarris Interactive survey for InterContinental Hotels & Resorts asked respondents, “When traveling internationally, do you generally venture out on your own to experience culture, or stick with your tour group and itineraries?” The survey found that 23% of the respondents stick with their
27. Consider a binomial experiment with n 20 and p .70.a. Compute f(12).b. Compute f(16).c. Compute P(x 16).d. Compute P(x 15).e. Compute E(x).f. Compute Var(x) and σ.
26. Consider a binomial experiment with n 10 and p .10.a. Compute f(0).b. Compute f(2).c. Compute P(x 2).d. Compute P(x 1).e. Compute E(x).f. Compute Var(x) and σ.
25. Consider a binomial experiment with two trials and p .4.a. Draw a tree diagram for this experiment (see Figure 5.3).b. Compute the probability of one success, f(1).c. Compute f(0).d. Compute f(2).e. Compute the probability of at least one success.f. Compute the expected value, variance, and
24. The J. R. Ryland Computer Company is considering a plant expansion to enable the company to begin production of a new computer product. The company’s president must determine whether to make the expansion a medium- or large-scale project. Demand for the new product is uncertain, which for
23. The 2002 New York City Housing and Vacancy Survey showed a total of 59,324 rentcontrolled housing units and 236,263 rent-stabilized units built in 1947 or later. For these rental units, the probability distributions for the number of persons living in the unit are given (http://www.census.gov,
22. The demand for a product of Carolina Industries varies greatly from month to month. The probability distribution in the following table, based on the past two years of data, shows the company’s monthly demand.a. If the company bases monthly orders on the expected value of the monthly demand,
21. The following probability distributions of job satisfaction scores for a sample of information systems (IS) senior executives and IS middle managers range from a low of 1 (very dissatisfied) to a high of 5 (very satisfied).a. What is the expected value of the job satisfaction score for senior
20. The probability distribution for damage claims paid by the Newton Automobile Insurance Company on collision insurance follows.a. Use the expected collision payment to determine the collision insurance premium that would enable the company to break even.b. The insurance company charges an annual
19. The National Basketball Association (NBA) records a variety of statistics for each team.Two of these statistics are the percentage of field goals made by the team and the percentage of three-point shots made by the team. For a portion of the 2004 season, the shooting records of the 29 teams in
18. TheAmericanHousingSurveyreportedthefollowingdataonthenumberofbedroomsinowneroccupied and renter-occupied houses in central cities (http://www.census.gov, March 31, 2003).a. Define a random variable x number of bedrooms in renter-occupied houses and develop a probability distribution for the
17. A volunteer ambulance service handles 0 to 5 service calls on any given day. The probability distribution for the number of service calls is as follows.a. What is the expected number of service calls?b. What is the variance in the number of service calls? What is the standard deviation?
16. The following table provides a probability distribution for the random variable y.a. Compute E( y).b. Compute Var( y) and σ.
15. The following table provides a probability distribution for the random variable x.a. Compute E(x), the expected value of x.b. Compute σ2 , the variance of x.c. Compute σ, the standard deviation of x.
12. The nation’s two biggest cable providers are Comcast Cable Communications, with 21.5 million subscribers, and Time Warner Cable, with 11.0 million subscribers (The New York Times 2007 Almanac). Suppose that management of Time Warner Cable subjectively assessed a probability distribution for
12. The nation’s two biggest cable providers are Comcast Cable Communications, with 21.5 million subscribers, and Time Warner Cable, with 11.0 million subscribers (The New York Times 2007 Almanac). Suppose that management of Time Warner Cable subjectively assessed a probability distribution for
11. A technician services mailing machines at companies in the Phoenix area. Depending on the type of malfunction, the service call can take 1, 2, 3, or 4 hours. The different types of malfunctions occur at about the same frequencya. Develop a probability distribution for the duration of a service
10. Table 5.4 shows the percent frequency distributions of job satisfaction scores for a sample of information systems (IS) senior executives and IS middle managers. The scores range from a low of 1 (very dissatisfied) to a high of 5 (very satisfied).a. Develop a probability distribution for the
9. Nationally, 38% of fourth-graders cannot read an age-appropriate book. The following data show the number of children, by age, identified as learning disabled under special education. Most of these children have reading problems that should be identified and corrected before third grade. Current
8. The following data were collected by counting the number of operating rooms in use at Tampa General Hospital over a 20-day period: On three of the days only one operating room was used, on five of the days two were used, on eight of the days three were used, and on four days all four of the
7. The probability distribution for the random variable x follows.a. Is this probability distribution valid? Explain.b. What is the probability that x 30?c. What is the probability that x is less than or equal to 25?d. What is the probability that x is greater than 30?
6. Listed is a series of experiments and associated random variables. In each case, identify the values that the random variable can assume and state whether the random variable is discrete or continuous.
5. To perform a certain type of blood analysis, lab technicians must perform two procedures.The first procedure requires either one or two separate steps, and the second procedure requires either one, two, or three steps.a. List the experimental outcomes associated with performing the blood
4. In November the U.S. unemployment rate was 4.5% (USA Today, January 4, 2007). The Census Bureau includes nine states in the Northeast region. Assume that the random variable of interest is the number of Northeast states with an unemployment rate in November that was less than 4.5%. What values
3. Three students scheduled interviews for summer employment at the Brookwood Institute.In each case the interview results in either an offer for a position or no offer. Experimental outcomes are defined in terms of the results of the three interviews.a. List the experimental outcomes.b. Define a
2. Consider the experiment of a worker assembling a product.a. Define a random variable that represents the time in minutes required to assemble the product.b. What values may the random variable assume?c. Is the random variable discrete or continuous?
1. Consider the experiment of tossing a coin twice.a. List the experimental outcomes.b. Define a random variable that represents the number of heads occurring on the two tosses.c. Show what value the random variable would assume for each of the experimental outcomes.d. Is this random variable
60. Companies that do business over the Internet can often obtain probability information about Web site visitors from previous Web sites visited. The article “Internet Marketing”(Interfaces, March/April 2001) described how clickstream data on Web sites visited could be used in conjunction with
59. An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities.a. What is the probability of finding oil?b. After 200 feet of drilling on the first well, a soil test is taken. The probabilities of finding the particular type of soil
58. A survey conducted by the Pew Internet & American Life Project showed that 8% of Internet users age 18 and older report keeping a blog. Referring to the 18–29 age group as young adults, the survey results showed that for bloggers 54% are young adults and for non-bloggers 24%are young adults
57. A company studied the number of lost-time accidents occurring at its Brownsville, Texas, plant. Historical records show that 6% of the employees suffered lost-time accidents last year. Management believes that a special safety program will reduce such accidents to 5%during the current year. In
56. Cooper Realty is a small real estate company located in Albany, New York, specializing primarily in residential listings. They recently became interested in determining the likelihood of one of their listings being sold within a certain number of days. An analysis of company sales of 800 homes
55. A large consumer goods company ran a television advertisement for one of its soap products. On the basis of a survey that was conducted, probabilities were assigned to the following events.The probabilities assigned were P(B) .20, P(S) .40, and P(B S) .12.a. What is the probability of
54. An IBD/TIPP poll conducted to learn about attitudes toward investment and retirement(Investor’s Business Daily, May 5, 2000) asked male and female respondents how important they felt level of risk was in choosing a retirement investment. The following joint probability table was constructed
53. Refer again to the data from the new-matriculants survey in exercise 52.a. Given that a person applied to more than one school, what is the probability that the person is 24–26 years old?b. Given that a person is in the 36-and-over age group, what is the probability that the person applied to
52. An MBA new-matriculants survey provided the following data for 2018 students.a. For a randomly selected MBA student, prepare a joint probability table for the experiment consisting of observing the student’s age and whether the student applied to one or more schools.b. What is the probability
51. The following crosstabulation shows household income by educational level of the head of household (Statistical Abstract of the United States: 2002).a. Develop a joint probability table.b. What is the probability of a head of household not being a high school graduate?c. What is the probability
50. A telephone survey to determine viewer response to a new television show obtained the following data.
49. A study of 31,000 hospital admissions in New York State found that 4% of the admissions led to treatment-caused injuries. One-seventh of these treatment-caused injuries resulted in death, and one-fourth were caused by negligence. Malpractice claims were filed in one out of 7.5 cases involving
48. In early 2003, President Bush proposed eliminating the taxation of dividends to shareholders on the grounds that it was double taxation. Corporations pay taxes on the earnings that are later paid out in dividends. In a poll of 671 Americans, TechnoMetrica Market Intelligence found that 47%
47. A financial manager made two new investments—one in the oil industry and one in municipal bonds. After a one-year period, each of the investments will be classified as either successful or unsuccessful. Consider the making of the two investments as an experiment.a. How many sample points
46. In a BusinessWeek/Harris Poll, 1035 adults were asked about their attitudes toward business (BusinessWeek, September 11, 2000). One question asked: “How would you rate large U.S. companies on making good products and competing in a global environment?”The responses were: excellent—18%,
45. In an article about investment growth, Money magazine reported that drug stocks show powerful long-term trends and offer investors unparalleled potential for strong and steady gains. The federal Health Care Financing Administration supports this conclusion through its forecast that annual
44. The American Council of Education reported that 47% of college freshmen earn a degree and graduate within five years (Associated Press, May 6, 2002). Assume that graduation records show women make up 50% of the students who graduated within five years, but only 45% of the students who did not
43. Small cars get better gas mileage, but they are not as safe as bigger cars. Small cars accounted for 18% of the vehicles on the road, but accidents involving small cars led to 11,898 fatalities during a recent year (Reader’s Digest, May 2000). Assume the probability a small car is involved in
42. A local bank reviewed its credit card policy with the intention of recalling some of its credit cards. In the past approximately 5% of cardholders defaulted, leaving the bank unable to collect the outstanding balance. Hence, management established a prior probability of .05 that any particular
41. A consulting firm submitted a bid for a large research project. The firm’s management initially felt they had a 50–50 chance of getting the project. However, the agency to which the bid was submitted subsequently requested additional information on the bid. Past experience indicates that
40. The prior probabilities for events A1, A2, and A3 are P(A1) .20, P(A2) .50, and P(A3) .30. The conditional probabilities of event B given A1, A2, and A3 are P(B A1) .50, P(B A2) .40, and P(B A3) .30.a. Compute P(B A1), P(B A2), and P(B A3).b. Apply Bayes’theorem,
39. The prior probabilities for events A1 and A2 are P(A1) .40 and P(A2) .60. It is also known that P(A1 A2) 0. Suppose P(B A1) .20 and P(B A2) .05.a. Are A1 and A2 mutually exclusive? Explain.b. Compute P(A1 B) and P(A2 B).c. Compute P(B).d. Apply Bayes’ theorem to compute
38. A Morgan Stanley Consumer Research Survey sampled men and women and asked each whether they preferred to drink plain bottled water or a sports drink such as Gatorade or Propel Fitness water (The Atlanta Journal-Constitution, December 28, 2005). Suppose 200 men and 200 women participated in the
37. Visa Card USA studied how frequently young consumers, ages 18 to 24, use plastic (debit and credit) cards in making purchases (Associated Press, January 16, 2006). The results of the study provided the following probabilities.
36. Reggie Miller of the Indiana Pacers is the National Basketball Association’s best career free throw shooter, making 89% of his shots (USA Today, January 22, 2004). Assume that late in a basketball game, Reggie Miller is fouled and is awarded two shots.a. What is the probability that he will
35. The U.S. Bureau of Labor Statistics collected data on the occupations of workers 25 to 64 years old. The following table shows the number of male and female workers (in millions) in each occupation category (Statistical Abstract of the United States: 2002).
34. The U.S. Department of Transportation reported that during November, 83.4% of Southwest Airlines flights, 75.1% of US Airways flights, and 70.1% of JetBlue flights arrived on time (USA Today, January 4, 2007). Assume that this on-time performance is applicable for flights arriving at concourse
33. In a survey of MBA students, the following data were obtained on “students’ first reason for application to the school in which they matriculated.”
32. Due to rising health insurance costs, 43 million people in the United States go without health insurance (Time, December 1, 2003). Sample data representative of the national health insurance coverage are shown here.a. Develop a joint probability table for these data and use the table to answer
31. Assume that we have two events, A and B, that are mutually exclusive. Assume further that we know P(A) .30 and P(B) .40.a. What is P(A B)?b. What is P(A B)?c. A student in statistics argues that the concepts of mutually exclusive events and independent events are really the same, and
30. Suppose that we have two events, A and B, with P(A) .50, P(B) .60, and P(A B) .40.a. Find P(A B).b. Find P(B A).c. Are A and B independent? Why or why not?
29. High school seniors with strong academic records apply to the nation’s most selective colleges in greater numbers each year. Because the number of slots remains relatively stable, some colleges reject more early applicants. The University of Pennsylvania received 2851 applications for early
28. Asurvey of magazine subscribers showed that 45.8% rented a car during the past 12 months for business reasons, 54% rented a car during the past 12 months for personal reasons, and 30% rented a car during the past 12 months for both business and personal reasons.a. What is the probability that a
27. A 2001 preseason NCAA football poll asked respondents to answer the question, “Will the Big Ten or the Pac-10 have a team in this year’s national championship game, the Rose Bowl?” Of the 13,429 respondents, 2961 said the Big Ten would, 4494 said the Pac-10 would, and 6823 said neither
26. Data on the 30 largest stock and balanced funds provided one-year and five-year percentage returns for the period ending March 31, 2000 (The Wall Street Journal,April 10, 2000).Suppose we consider a one-year return in excess of 50% to be high and a five-year return in excess of 300% to be high.
25. The U.S. Census Bureau provides data on the number of young adults, ages 18–24, who are living in their parents’ home.* Let M the event a male young adult is living in his parents’ home F the event a female young adult is living in her parents’ home If we randomly select a male
24. Clarkson University surveyed alumni to learn more about what they think of Clarkson. One part of the survey asked respondents to indicate whether their overall experience at Clarkson fell short of expectations, met expectations, or surpassed expectations. The results showed that 4% of the
23. Suppose that we have a sample space S {E1, E2, E3, E4, E5, E6, E7}, where E1, E2,..., E7 denote the sample points. The following probability assignments apply: P(E1) .05, P(E2) .20, P(E3) .20, P(E4) .25, P(E5) .15, P(E6) .10, and P(E7) .05. Leta. Find P(A), P(B), and P(C).b.
22. Suppose that we have a sample space with five equally likely experimental outcomes: E1, E2, E3, E4, E5. Leta. Find P(A), P(B), and P(C).b. Find P(A B). Are A and B mutually exclusive?c. Find Ac, Cc, P(Ac), and P(Cc).d. Find A Bc and P(A Bc).e. Find P(B C).
21. The U.S. population by age is as follows (The World Almanac, 2004). The data are in millions of people.
20. Fortune magazine publishes an annual list of the 500 largest companies in the United States.The following data show the five states with the largest number of Fortune 500 companies(The New York Times Almanac, 2006).Suppose a Fortune 500 company is chosen for a follow-up questionnaire. What are
19. The National Sporting Goods Association conducted a survey of persons 7 years of age or older about participation in sports activities (Statistical Abstract of the United States: 2002).The total population in this age group was reported at 248.5 million, with 120.9 million male and 127.6
18. To investigate how often we eat at home as a family during the week, Harris Interactive surveyed 496 adults living with children under the age of 18 (USA Today,January 3, 2007).The survey results are shown in the following table.
17. Refer to the KP&L sample points and sample point probabilities in Tables 4.2 and 4.3.a. The design stage (stage 1) will run over budget if it takes 4 months to complete. List the sample points in the event the design stage is over budget.b. What is the probability that the design stage is over
16. Consider the experiment of rolling a pair of dice. Suppose that we are interested in the sum of the face values showing on the dice.a. How many sample points are possible? (Hint: Use the counting rule for multiple-step experiments.)b. List the sample points.c. What is the probability of
15. Consider the experiment of selecting a playing card from a deck of 52 playing cards. Each card corresponds to a sample point with a 1/52 probability.a. List the sample points in the event an ace is selected.b. List the sample points in the event a club is selected.c. List the sample points in

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