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business statistics communicating

Statistics For Business And Economics 10th Edition David R. Anderson, Dennis J. Sweeney, Thomas A. Williams - Solutions

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,
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 (www.census.gov, January
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.Unit Demand Probability 300 .20 400 .30 500 .35 600 .15a. If the company bases
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.Payment ($) Probability 0 .85 500 .04 1000 .04 3000 .03 5000 .02 8000 .01 10000 .01a. Use the expected collision payment to determine the collision insurance premium
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. The American Housing Survey reported the following data on the number of bed rooms in owner occupied and renter-occupied houses in central cities (www.census.gov, March 31, 2003).a. Define a random variable x number of bedrooms in renter-occupied houses and develop a probability distribution
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? Number
16. The following table provides a probability distribution for the random variable y.y f( y)2 .20 4 .30 7 .40 8 .10a. Compute E( y).b. Compute Var( y) and σ.
15. The following table provides a probability distribution for the random variable x.x f(x)3 .25 6 .50 9 .25a. Compute E(x), the expected value of x.b. Compute σ2, the variance of x.c. Compute σ, the standard deviation of x.
14. The following table is a partial probability distribution for the MRA Company’s projected profits (x profit in $1000s) for the first year of operation (the negative value denotes a loss).a. What is the proper value for f (200)? What is your interpretation of this value?b. What is the
13. Apsychologist determined that the number of sessions required to obtain the trust of a new patient is either 1, 2, or 3. Let x be a random variable indicating the number of sessions required to gain the patient’s trust. The following probability function has been proposed.a. Is this
12. The director of admissions at Lakeville Community College subjectively assessed a probability distribution for x, the number of entering students, as follows.x f(x)1000 .15 1100 .20 1200 .30 1300 .25 1400 .10a. Is this probability distribution valid? Explain.b. What is the probability of 1200
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 frequency.a. 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.x f(x)20 .20 25 .15 30 .25 35 .40a. 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
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.Experiment Random Variable (x)a. Take a 20-question examination Number of questions answered
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. Suppose we know home mortgage rates for 12 Florida lending institutions. Assume that the random variable of interest is the number of lending institutions in this group that offers a 30-year fixed rate of 8.5% or less. What values may this random variable assume?
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.P(high-quality oil) = .50 P(medium-quality oil) = .20 P(no oil) = .30a. What is the probability of finding oil?b. After 200 feet of drilling on the first well, a soil
58. The Dallas IRS auditing staff, concerned with identifying potentially fraudulent tax returns, believes that the probability of finding a fraudulent return given that the return contains deductions for contributions exceeding the IRS standard is .20. Given that the deductions for contributions
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.B = individual purchased the product S = individual recalls seeing the advertisement B ∩ S = individual
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 GMAC 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
52. A GMAC 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
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.Rating Frequency Poor 4 Below average 8 Average 11 Above average 14 Excellent 13a. What is the probability that a randomly selected viewer will rate the new show as average or better?b. What is
49. Astudy 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. Alocal 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.• The probability that a consumer uses a plastic card when making a
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).a. Develop a joint probability table.b.
34. The following table shows the probabilities of blood types in the general population(Hoxworth Blood Center, Cincinnati, Ohio, March 2003).a. What is the probability a person will have type O blood?b. What is the probability a person will be Rh?c. What is the probability a person will be Rh
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.”a. Develop a joint probability table for these data.b. Use the marginal probabilities of school quality, school cost or convenience, and other
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. A2001 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 the
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
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. Let a. Find P(A), P(B), and P(C). b. Find
22. Suppose that we have a sample space with five equally likely experimental outcomes: E1, E2, E3, E4, E5. Let a. Find P(A), P(B), and P(C). A = {E1, E2} B = {E3, E} C = {E2, E3, Es} b. Find P(AUB). Are A and B mutually exclusive? c. Find A, C, P(A), and P(C). d. Find A U B and P(A U B). e. Find
21. The U.S. population by age is as follows (The World Almanac 2004). The data are in millions of people.Age Number 19 and under 80.5 20 to 24 19.0 25 to 34 39.9 35 to 44 45.2 45 to 54 37.7 55 to 64 24.3 65 and over 35.0 Assume that a person will be randomly chosen from this population.a. What is
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).Number of State Companies New York 54 California 52 Texas 48 Illinois 33 Ohio 30
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. Suppose that a manager of a large apartment complex provides the following subjective probability estimates about the number of vacancies that will exist next month.Vacancies Probability 0 .05 1 .15 2 .35 3 .25 4 .10 5 .10 Provide the probability of each of the following events.a. No
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
14. An experiment has four equally likely outcomes: E1, E2, E3, and E4.a. What is the probability that E2 occurs?b. What is the probability that any two of the outcomes occur (e.g., E1 or E3)?c. What is the probability that any three of the outcomes occur (e.g., E1 or E2 or E4)?
13. A company that manufactures toothpaste is studying five different package designs.Assuming that one design is just as likely to be selected by a consumer as any other design, what selection probability would you assign to each of the package designs? In an actual experiment, 100 consumers were
12. The Powerball lottery is played twice each week in 28 states, the Virgin Islands, and the District of Columbia. To play Powerball a participant must purchase a ticket and then select five numbers from the digits 1 through 55 and a Powerball number from the digits 1 through 42. To determine the
11. The National Highway Traffic Safety Administration (NHTSA) conducted a survey to learn about how drivers throughout the United States are using seat belts (Associated Press, August 25, 2003). Sample data consistent with the NHTSA survey are as follows.a. For the United States, what is the
10. Venture capital can provide a big boost in funds available to companies. According to Venture Economics (Investor’s Business Daily, April 28, 2000), of 2374 venture capital disbursements, 1434 were to companies in California, 390 were to companies in Massachusetts, 217 were to companies in
9. Simple random sampling uses a sample of size n from a population of size N to obtain data that can be used to make inferences about the characteristics of a population. Suppose that, from a population of 50 bank accounts, we want to take a random sample of four accounts in order to learn about
8. In the city of Milford, applications for zoning changes go through a two-step process: a review by the planning commission and a final decision by the city council. At step 1 the planning commission reviews the zoning change request and makes a positive or negative recommendation concerning the
7. Adecision maker subjectively assigned the following probabilities to the four outcomes of an experiment: P(E1) .10, P(E2) .15, P(E3) .40, and P(E4) .20. Are these probability assignments valid? Explain.
6. An experiment with three outcomes has been repeated 50 times, and it was learned that E1 occurred 20 times, E2 occurred 13 times, and E3 occurred 17 times. Assign probabilities to the outcomes. What method did you use?
5. Suppose an experiment has five equally likely outcomes: E1, E2, E3, E4, E5. Assign probabilities to each outcome and show that the requirements in equations (4.3) and (4.4) are satisfied. What method did you use?
4. Consider the experiment of tossing a coin three times.a. Develop a tree diagram for the experiment.b. List the experimental outcomes.c. What is the probability for each experimental outcome?
3. How many permutations of three items can be selected from a group of six? Use the letters A, B, C, D, E, and F to identify the items, and list each of the permutations of items B, D, and F.
2. How many ways can three items be selected from a group of six items? Use the letters A, B, C, D, E, and F to identify the items, and list each of the different combinations of three items.
1. An experiment has three steps with three outcomes possible for the first step, two outcomes possible for the second step, and four outcomes possible for the third step. How many experimental outcomes exist for the entire experiment?
70. Automobiles traveling on a road with a posted speed limit of 55 miles per hour are checked for speed by a state police radar system. Following is a frequency distribution of speeds.Speed (miles per hour) Frequency 45–49 10 50–54 40 55–59 150 60–64 175 65–69 75 70–74 15 75–79 10
69. The days to maturity for a sample of five money market funds are shown here. The dollar amounts invested in the funds are provided. Use the weighted mean to determine the mean number of days to maturity for dollars invested in these five money market funds.Days to Dollar Value Maturity
68. A forecasting technique referred to as moving averages uses the average or mean of the most recent n periods to forecast the next value for time series data. With a three-period moving average, the most recent three periods of data are used in the forecast computation.Consider a product with
67. The following data show the trailing 52-week primary share earnings and book values as reported by 10 companies (The Wall Street Journal, March 13, 2000).a. Develop a scatter diagram for the data with book value on the x-axis.b. What is the sample correlation coefficient, and what does it tell
66. Road & Track provided the following sample of the tire ratings and load-carrying capacity of automobiles tires.Tire Rating Load-Carrying Capacity 75 853 82 1047 85 1135 87 1201 88 1235 91 1356 92 1389 93 1433 105 2039a. Develop a scatter diagram for the data with tire rating on the x-axis.b.
65. The following data show the media expenditures ($ millions) and shipments in millions of barrels (bbls.) for 10 major brands of beer.a. What is the sample covariance? Does it indicate a positive or negative relationship?b. What is the sample correlation coefficient? Brand Budweiser Bud Light
64. The National Association of Realtors reported the median home price in the United States and the increase in median home price over a five-year period (The Wall Street Journal, January 16, 2006). Use the sample home prices shown here to answer the following questions.a. What is the sample
63. Public transportation and the automobile are two methods an employee can use to get towork each day. Samples of times recorded for each method are shown. Times are in minutes.a. Compute the sample mean time to get to work for each method.b. Compute the sample standard deviation for each
62. Small business owners often look to payroll service companies to handle their employee payroll. Reasons are that small business owners face complicated tax regulations and penalties for employment tax errors are costly. According to the Internal Revenue Service, 26% of all small business
61. The U.S. Department of Education reports that about 50% of all college students use a student loan to help cover college expenses (National Center for Educational Studies, January 2006). A sample of students who graduated with student loan debt is shown here.The data, in thousands of dollars,
60. Dividend yield is the annual dividend per share a company pays divided by the current market price per share expressed as a percentage. Asample of 10 large companies provided the following dividend yield data (The Wall Street Journal, January 16, 2004).a. What are the mean and median dividend
59. The U.S. Census Bureau provides statistics on family life in the United States, including the age at the time of first marriage, current marital status, and size of household(www.census.gov, March 20, 2006). The following data show the age at the time of first marriage for a sample of men and a

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