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Statistics For Business And Economics 10th Edition David R. Anderson, Dennis J. Sweeney, Thomas A. Williams - Solutions
8. The following list provides the NCAA top 25 football teams for the 2002 season (NCAA News, January 4, 2003). Use the ninth column of the random numbers in Table 7.1, beginning with 13554, to select a simple random sample of six football teams. Begin with team 13 and use the first two digits in
7. Assume that we want to identify a simple random sample of 12 of the 372 doctors practicing in a particular city. The doctors’ names are available from a local medical organization.Use the eighth column of five-digit random numbers in Table 7.1 to identify the 12 doctors for the sample. Ignore
6. The County and City Data Book, published by the Census Bureau, lists information on 3139 counties throughout the United States. Assume that a national study will collect data from 30 randomly selected counties. Use four-digit random numbers from the last column of Table 7.1 to identify the
5. A student government organization is interested in estimating the proportion of students who favor a mandatory “pass-fail” grading policy for elective courses. A list of names and addresses of the 645 students enrolled during the current quarter is available from the registrar’s office.
4. The 10 most active stocks on the New York Stock Exchange on March 6, 2006, are shown here (The Wall Street Journal, March 7, 2006).Exchange authorities decided to investigate trading practices using a sample of three of these stocks.a. Beginning with the first random digit in column 6 of Table
3. Fortune publishes data on sales, profits, assets, stockholders’ equity, market value, and earnings per share for the 500 largest U.S. industrial corporations (Fortune 500, 2003).Assume that you want to select a simple random sample of 10 corporations from the Fortune 500 list. Use the last
2. Assume a finite population has 350 elements. Using the last three digits of each of the following five-digit random numbers (e.g.; 601, 022, 448, . . . ), determine the first four elements that will be selected for the simple random sample. 98601 73022 83448 02147 34229 27553 84147 93289 14209
1. Consider a finite population with five elements labeled A, B, C, D, and E. Ten possible simple random samples of size 2 can be selected.a. List the 10 samples beginning with AB, AC, and so on.b. Using simple random sampling, what is the probability that each sample of size 2 is selected?c.
54. The time (in minutes) between telephone calls at an insurance claims office has the following exponential probability distribution.f (x) = .50e.50x for x 0a. What is the mean time between telephone calls?b. What is the probability of having 30 seconds or less between telephone calls?c. What is
53. The average travel time to work for New York City residents is 36.5 minutes (Time Almanac, 2001).a. Assume the exponential probability distribution is applicable and show the probability density function for the travel time to work for a typical New Yorker.b. What is the probability it will
52. The Web site for the Bed and Breakfast Inns of North America (www.cimarron.net) gets approximately seven visitors per minute (Time, September 2001). Suppose the number of Web site visitors per minute follows a Poisson probability distribution.a. What is the mean time between visits to the Web
51. The time in minutes for which a student uses a computer terminal at the computer center of a major university follows an exponential probability distribution with a mean of 36 minutes. Assume a student arrives at the terminal just as another student is beginning to work on the terminal.a. What
50. A blackjack player at a Las Vegas casino learned that the house will provide a free room if play is for four hours at an average bet of $50. The player’s strategy provides a probability of .49 of winning on any one hand, and the player knows that there are 60 hands per hour. Suppose the
49. Consider a multiple-choice examination with 50 questions. Each question has four possible answers. Assume that a student who has done the homework and attended lectures has a 75% probability of answering any question correctly.a. A student must answer 43 or more questions correctly to obtain a
48. A machine fills containers with a particular product. The standard deviation of filling weights is known from past data to be .6 ounce. If only 2% of the containers hold less than 18 ounces, what is the mean filling weight for the machine? That is, what must μ equal?Assume the filling weights
47. According to Advertising Age, the average base salary for women working as copywriters in advertising firms is higher than the average base salary for men. The average base salary for women is $67,000 and the average base salary for men is $65,500 (Working Woman, July/August 2000). Assume
46. Assume that the test scores from a college admissions test are normally distributed, with a mean of 450 and a standard deviation of 100.a. What percentage of the people taking the test score between 400 and 500?b. Suppose someone receives a score of 630. What percentage of the people taking the
45. Is lack of sleep causing traffic fatalities? Astudy conducted under the auspices of the National Highway Traffic Safety Administration found that the average number of fatal crashes caused by drowsy drivers each year was 1550 (BusinessWeek, January 26, 2004). Assume the annual number of fatal
44. Ward Doering Auto Sales is considering offering a special service contract that will cover the total cost of any service work required on leased vehicles. From experience, the company manager estimates that yearly service costs are approximately normally distributed, with a mean of $150 and a
43. Condé Nast Traveler publishes a Gold List of the top hotels all over the world. The Broadmoor Hotel in Colorado Springs contains 700 rooms and is on the 2004 Gold List (CondéNast Traveler, January 2004). Suppose Broadmoor’s marketing group forecasts a mean demand of 670 rooms for the coming
42. The average annual amount American households spend for daily transportation is $6312(Money, August 2001). Assume that the amount spent is normally distributed.a. Suppose you learn that 5% of American households spend less than $1000 for daily transportation. What is the standard deviation of
41. Motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production process. Assume a production process produces items with a mean weight of 10 ounces. Calculate the probability of a defect and the expected number of defects for a
40. The U.S. Bureau of Labor Statistics reports that the average annual expenditure on food and drink for all families is $5700 (Money, December 2003). Assume that annual expenditure on food and drink is normally distributed and that the standard deviation is $1500.a. What is the range of
39. A business executive, transferred from Chicago to Atlanta, needs to sell her house in Chicago quickly. The executive’s employer has offered to buy the house for $210,000, but the offer expires at the end of the week. The executive does not currently have a better offer, but can afford to
38. Do interruptions while you are working reduce your productivity? According to a University of California–Irvine study, businesspeople are interrupted at the rate of approximately 51⁄2 times per hour (Fortune, March 20, 2006). Suppose the number of interruptions follows a Poisson probability
37. Sparagowski & Associates conducted a study of service times at the drive-up window of fast-food restaurants. The average service time at McDonald’s restaurants was 2.78 minutes(The Cincinnati Enquirer, July 9, 2000). Service times such as these frequently follow an exponential distribution.a.
36. The lifetime (hours) of an electronic device is a random variable with the following exponential probability density function.a. What is the mean lifetime of the device?b. What is the probability that the device will fail in the first 25 hours of operation?c. What is the probability that the
35. The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 12 seconds.a. Sketch this exponential probability distribution.b. What is the probability that the arrival time between vehicles is 12 seconds or less?c. What is the
34. The time required to pass through security screening at the airport can be annoying to travelers.The mean wait time during peak periods at Cincinnati/Northern Kentucky International Airport is 12.1 minutes (The Cincinnati Enquirer, February 2, 2006). Assume the time to pass through security
33. Consider the following exponential probability density function. f(x) = 1-e-x13 for x 0 a. Write the formula for P(xx). b. Find P(x 2). c. Find P(x 3). d. Find P(x5). e. Find P(2x5).
32. Consider the following exponential probability density function. a. Find P(X 6). b. Find P(x4). c. Find P(x6). d. Find P(4x6). f(x) = = - e-x/8 =je-x18 for x 0
31. A Myrtle Beach resort hotel has 120 rooms. In the spring months, hotel room occupancy is approximately 75%.a. What is the probability that at least half of the rooms are occupied on a given day?b. What is the probability that 100 or more rooms are occupied on a given day?c. What is the
30. When you sign up for a credit card, do you read the contract carefully? In a FindLaw.com survey, individuals were asked, “How closely do you read a contract for a credit card?”(USA Today, October 16, 2003). The findings were that 44% read every word, 33% read enough to understand the
29. The unemployment rate is 5.8% (Bureau of Labor Statistics, www.bls.gov, April 3, 2003).Suppose that 100 employable people are selected randomly.a. What is the expected number who are unemployed?b. What are the variance and standard deviation of the number who are unemployed?c. What is the
28. President Bush proposed the elimination of taxes on dividends paid to shareholders on the grounds that they result in double taxation. The earnings used to pay dividends are already taxed to the corporation. A survey on this issue revealed that 47% of Americans favor the proposal. By political
27. Assume a binomial probability distribution has p .60 and n 200.a. What are the mean and standard deviation?b. Is this situation one in which binomial probabilities can be approximated by the normal probability distribution? Explain.c. What is the probability of 100 to 110 successes?d. What
26. A binomial probability distribution has p .20 and n 100.a. What are the mean and standard deviation?b. Is this situation one in which binomial probabilities can be approximated by the normal probability distribution? Explain.c. What is the probability of exactly 24 successes?d. What is the
25. According to the Sleep Foundation, the average night’s sleep is 6.8 hours (Fortune, March 20, 2006). Assume the standard deviation is .6 hours and that the probability distribution is normal.a. What is the probability that a randomly selected person sleeps more than 8 hours?b. What is the
24. Trading volume on the New York Stock Exchange is heaviest during the first half hour(early morning) and last half hour (late afternoon) of the trading day. The early morning trading volumes (millions of shares) for 13 days in January and February are shown here(Barron’s, January 23, 2006;
23. The time needed to complete a final examination in a particular college course is normally distributed with a mean of 80 minutes and a standard deviation of 10 minutes. Answer the following questions.a. What is the probability of completing the exam in one hour or less?b. What is the
22. The mean hourly pay rate for financial managers in the East North Central region is $32.62, and the standard deviation is $2.32 (Bureau of Labor Statistics, September 2005). Assume that pay rates are normally distributed.a. What is the probability a financial manager earns between $30 and $35
21. A person must score in the upper 2% of the population on an IQ test to qualify for membership in Mensa, the international high-IQ society (U.S. Airways Attaché, September 2000). If IQ scores are normally distributed with a mean of 100 and a standard deviation of 15, what score must a person
20. In January 2003, the American worker spent an average of 77 hours logged on to the Internet while at work (CNBC, March 15, 2003). Assume the population mean is 77 hours, the times are normally distributed, and that the standard deviation is 20 hours.a. What is the probability that in January
19. The average amount of precipitation in Dallas, Texas, during the month of April is 3.5 inches(The World Almanac, 2000). Assume that a normal distribution applies and that the standard deviation is .8 inches.a. What percentage of the time does the amount of rainfall in April exceed 5 inches?b.
18. The average stock price for companies making up the S&P 500 is $30, and the standard deviation is $8.20 (BusinessWeek, Special Annual Issue, Spring 2003). Assume the stock prices are normally distributed.a. What is the probability a company will have a stock price of at least $40?b. What is the
17. For borrowers with good credit scores, the mean debt for revolving and installment accounts is $15,015 (BusinessWeek, March 20, 2006). Assume the standard deviation is$3540 and that debt amounts are normally distributed.a. What is the probability that the debt for a randomly selected borrower
16. Given that z is a standard normal random variable, find z for each situation.a. The area to the right of z is .01.b. The area to the right of z is .025.c. The area to the right of z is .05.d. The area to the right of z is .10.
15. Given that z is a standard normal random variable, find z for each situation.a. The area to the left of z is .2119.b. The area between z and z is .9030.c. The area between z and z is .2052.d. The area to the left of z is .9948.e. The area to the right of z is .6915.
14. Given that z is a standard normal random variable, find z for each situation.a. The area to the left of z is .9750.b. The area between 0 and z is .4750.c. The area to the left of z is .7291.d. The area to the right of z is .1314.e. The area to the left of z is .6700.f. The area to the right of
13. Given that z is a standard normal random variable, compute the following probabilities.a. P(1.98 z .49)b. P(.52 z 1.22)c. P(1.75 z 1.04)
12. Given that z is a standard normal random variable, compute the following probabilities.a. P(0 z .83)b. P(1.57 z 0)c. P(z .44)d. P(z .23)e. P(z 1.20)f. P(z .71)
11. Given that z is a standard normal random variable, compute the following probabilities.a. P(z 1.0)b. P(z 1)c. P(z 1.5)d. P(2.5 z)e. P(3 z 0)
10. Draw a graph for the standard normal distribution. Label the horizontal axis at values of3, 2, 1, 0, 1, 2, and 3. Then use the table of probabilities for the standard normal distribution inside the front cover of the text to compute the following probabilities.a. P(z 1.5)b. P(z 1)c. P(1 z
9. A random variable is normally distributed with a mean of μ 50 and a standard deviation of σ 5.a. Sketch a normal curve for the probability density function. Label the horizontal axis with values of 35, 40, 45, 50, 55, 60, and 65. Figure 6.4 shows that the normal curve almost touches the
8. Using Figure 6.4 as a guide, sketch a normal curve for a random variable x that has a mean of μ 100 and a standard deviation of σ 10. Label the horizontal axis with values of 70, 80, 90, 100, 110, 120, and 130.
7. Suppose we are interested in bidding on a piece of land and we know one other bidder is interested.* The seller announced that the highest bid in excess of $10,000 will be accepted.Assume that the competitor’s bid x is a random variable that is uniformly distributed between $10,000 and
6. The label on a bottle of liquid detergent shows the contents to be 12 ounces per bottle. The production operation fills the bottle uniformly according to the following probability density function.a. What is the probability that a bottle will be filled with between 12 and 12.05 ounces?b. What is
5. The driving distance for the top 100 golfers on the PGA tour is between 284.7 and 310.6 yards (Golfweek, March 29, 2003). Assume that the driving distance for these golfers is uniformly distributed over this interval.a. Give a mathematical expression for the probability density function of
4. Most computer languages include a function that can be used to generate random numbers.In Excel, the RAND function can be used to generate random numbers between 0 and 1. If we let x denote a random number generated using RAND, then x is a continuous random variable with the following
3. Delta Airlines quotes a flight time of 2 hours, 5 minutes for its flights from Cincinnati to Tampa. Suppose we believe that actual flight times are uniformly distributed between 2 hours and 2 hours, 20 minutes.a. Show the graph of the probability density function for flight time.b. What is the
2. The random variable x is known to be uniformly distributed between 10 and 20.a. Show the graph of the probability density function.b. Compute P(x 15).c. Compute P(12 x 18).d. Compute E(x).e. Compute Var(x).
1. The random variable x is known to be uniformly distributed between 1.0 and 1.5.a. Show the graph of the probability density function.b. Compute P(x 1.25).c. Compute P(1.0 x 1.25).d. Compute P(1.20 x 1.5).
66. Through the week ending September 16, 2001, Tiger Woods was the leading money winner on the PGA Tour, with total earnings of $5,517,777. Of the top 10 money winners, seven players used a Titleist brand golf ball (www.pgatour.com). Suppose that we randomly select two of the top 10 money
65. A deck of playing cards contains 52 cards, four of which are aces. What is the probability that the deal of a five-card hand provides:a. A pair of aces?b. Exactly one ace?c. No aces?d. At least one ace?
64. Customer arrivals at a bank are random and independent; the probability of an arrival in any one-minute period is the same as the probability of an arrival in any other one-minute period.Answer the following questions, assuming a mean arrival rate of three customers per minute.a. What is the
63. A regional director responsible for business development in the state of Pennsylvania is concerned about the number of small business failures. If the mean number of small business failures per month is 10, what is the probability that exactly four small businesses will fail during a given
62. Anew automated production process averages 1.5 breakdowns per day. Because of the cost associated with a breakdown, management is concerned about the possibility of having three or more breakdowns during a day. Assume that breakdowns occur randomly, that the probability of a breakdown is the
61. Cars arrive at a car wash randomly and independently; the probability of an arrival is the same for any two time intervals of equal length. The mean arrival rate is 15 cars per hour.What is the probability that 20 or more cars will arrive during any given hour of operation?
60. A poll conducted by Zogby International showed that of those Americans who said music plays a “very important” role in their lives, 30% said their local radio stations “always”play the kind of music they like (www.zogby.com, January 12, 2004). Suppose a sample of 800 people who say
59. The unemployment rate is 4.1% (Barron’s, September 4, 2000). Assume that 100 employable people are selected randomly.a. What is the expected number of people who are unemployed?b. What are the variance and standard deviation of the number of people who are unemployed?
58. Many companies use a quality control technique called acceptance sampling to monitor incoming shipments of parts, raw materials, and so on. In the electronics industry, component parts are commonly shipped from suppliers in large lots. Inspection of a sample of n components can be viewed as the
57. A company is planning to interview Internet users to learn how its proposed Web site will be received by different age groups. According to the Census Bureau, 40% of individuals ages 18 to 54 and 12% of individuals age 55 and older use the Internet (Statistical Abstract of the United States,
56. A survey conducted by the Bureau of Transportation Statistics (BTS) showed that the average commuter spends about 26 minutes on a one-way door-to-door trip from home to work. In addition, 5% of commuters reported a one-way commute of more than one hour(www.bts.gov, January 12, 2004).a. If 20
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 (www.gallup.com, January 3, 2004). Assume that in a group of 10 individuals, seven preferred football
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 (www.bestinns.net), which averages approximately seven visitors per minute, enables many B&Bs to attract guests (Time, September 2001).a. Compute the probability
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. For the special case of a binomial random variable, we stated that the variance could be computed using the formula σ2 np(1 p). For the Martin Clothing Store problem with n 3 and p .3 we found σ2 np(1 p) 3(.3)(.7) .63. Use the general definition of variance for a discrete
35. Auniversity 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.Areliability 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
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