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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
35. The president of Doerman Distributors, Inc., believes that 30% of the firm’s orders come from first-time customers. A simple random sample of 100 orders will be used to estimate the proportion of first-time customers.a. Assume that the president is correct and p .30. What is the sampling
34. The population proportion is .30. What is the probability that a sample proportion will be within .04 of the population proportion for each of the following sample sizes?a. n 100b. n 200c. n 500d. n 1000e. What is the advantage of a larger sample size?
33. Assume that the population proportion is .55. Compute the standard error of the proportion, , for sample sizes of 100, 200, 500, and 1000. What can you say about the size of the standard error of the proportion as the sample size is increased?
32. A population proportion is .40. A simple random sample of size 200 will be taken and the sample proportion will be used to estimate the population proportion.a. What is the probability that the sample proportion will be within .03 of the population proportion?b. What is the probability that
31. A simple random sample of size 100 is selected from a population with p .40.a. What is the expected value of ?b. What is the standard error of ?c. Show the sampling distribution of .d. What does the sampling distribution of show?
30. To estimate the mean age for a population of 4000 employees, a simple random sample of 40 employees is selected.a. Would you use the finite population correction factor in calculating the standard error of the mean? Explain.b. If the population standard deviation is σ 8.2 years, compute the
29. The average price of a gallon of unleaded regular gasoline was reported to be $2.34 in northern Kentucky (The Cincinnati Enquirer, January 21, 2006). Use this price as the population mean, and assume the population standard deviation is $.20.a. What is the probability that the mean price for a
28. The average score for male golfers is 95 and the average score for female golfers is 106(Golf Digest, April 2006). Use these values as the population means for men and women and assume that the population standard deviation is σ 14 strokes for both. A simple random sample of 30 male golfers
27. BusinessWeek conducted a survey of graduates from 30 top MBA programs (BusinessWeek, September 22, 2003). On the basis of the survey, assume that the mean annual salary for male and female graduates 10 years after graduation is $168,000 and $117,000, respectively. Assume the standard deviation
26. The mean annual cost of automobile insurance is $939 (CNBC, February 23, 2006).Assume that the standard deviation is σ $245.a. What is the probability that a simple random sample of automobile insurance policies will have a sample mean within $25 of the population mean for each of the
25. The College Board American College Testing Program reported a population mean SAT score of μ 1020 (The World Almanac 2003). Assume that the population standard deviation is σ 100.a. What is the probability that a random sample of 75 students will provide a sample mean SAT score within 10
24. The mean tuition cost at state universities throughout the United States is $4260 per year(St. Petersburg Times, December 11, 2002). Use this value as the population mean and assume that the population standard deviation is σ $900. Suppose that a random sample of 50 state universities will
23. In the EAI sampling problem (see Figure 7.5), we showed that for n 30, there was .5034 probability of obtaining a sample mean within $500 of the population mean.a. What is the probability that is within $500 of the population mean if a sample of size 60 is used?b. Answer part (a) for a
22. Refer to the EAI sampling problem. Suppose a simple random sample of 60 managers is used.a. Sketch the sampling distribution of when simple random samples of size 60 are used.b. What happens to the sampling distribution of if simple random samples of size 120 are used?c. What general statement
21. Suppose a simple random sample of size 50 is selected from a population with σ 10.Find the value of the standard error of the mean in each of the following cases (use the finite population correction factor if appropriate).a. The population size is infinite.b. The population size is N
20. Assume the population standard deviation is σ 25. Compute the standard error of the mean, , for sample sizes of 50, 100, 150, and 200. What can you say about the size of the standard error of the mean as the sample size is increased?
19. A population has a mean of 200 and a standard deviation of 50. Suppose a simple random sample of size 100 is selected and is used to estimate μ.a. What is the probability that the sample mean will be within 5 of the population mean?b. What is the probability that the sample meanwill
18. A population has a mean of 200 and a standard deviation of 50. A simple random sample of size 100 will be taken and the sample mean will be used to estimate the population mean.a. What is the expected value of ?b. What is the standard deviation of ?c. Show the sampling distribution of .d. What
17. The American Association of Individual Investors (AAII) polls its subscribers on a weekly basis to determine the number who are bullish, bearish, or neutral on the short-term prospects for the stock market. Their findings for the week ending March 2, 2006, are consistent with the following
16. A sample of 50 Fortune 500 companies (Fortune, April 14, 2003) showed 5 were based in New York, 6 in California, 2 in Minnesota, and 1 in Wisconsin.a. Develop an estimate of the proportion of Fortune 500 companies based in New York.b. Develop an estimate of the number of Fortune 500 companies
15. Many drugs used to treat cancer are expensive. BusinessWeek reported on the cost per treatment of Herceptin, a drug used to treat breast cancer (BusinessWeek, January 30, 2006).Typical treatment costs (in dollars) for Herceptin are provided by a simple random sample of 10 patients.4376 5578
14. BusinessWeek published information on 283 equity mutual funds (BusinessWeek, January 26, 2004). A sample of 40 of those funds is contained in the data set MutualFund. Use the data set to answer the following questions.a. Develop a point estimate of the proportion of the BusinessWeek equity
13. A simple random sample of 5 months of sales data provided the following information:Month: 1 2345 Units Sold: 94 100 85 94 92a. Develop a point estimate of the population mean number of units sold per month.b. Develop a point estimate of the population standard deviation.
12. A survey question for a sample of 150 individuals yielded 75 Yes responses, 55 No responses, and 20 No Opinions.a. What is the point estimate of the proportion in the population who respond Yes?b. What is the point estimate of the proportion in the population who respond No?
11. The following data are from a simple random sample.5 8 10 7 10 14a. What is the point estimate of the population mean?b. What is the point estimate of the population standard deviation?
10. Indicate which of the following situations involve sampling from a finite population and which involve sampling from a process. In cases where the sampled population is finite, describe how you would construct a frame.a. Obtain a sample of licensed drivers in the state of New York.b. Obtain a
9. The Wall Street Journal provides the net asset value, the year-to-date percent return, and the three-year percent return for 555 mutual funds (The Wall Street Journal, April 25, 2003). Assume that a simple random sample of 12 of the 555 mutual funds will be selected for a follow-up study on the
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).AT&T Lucent Nortel Qwest Bell South Pfizer Texas Instruments Gen. Elect. iShrMSJpn LSI Logic Exchange authorities decided to investigate trading practices using a
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, 2006). 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.a. 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 the probability of
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 (http://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
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
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 a 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 leave
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
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.a. Write the formula for P(x x0).b. Find P(x 2).c. Find P(x 3).d. Find P(x 5).e. Find P(2 x5).
32. Consider the following exponential probability density function.a. Find P(x 6).b. Find P(x 4).c. Find P(x 6).d. Find P(4 x6).
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, http://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
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.
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 z1.22)c. P(1.75 z1.04)
12. Given that z is a standard normal random variable, compute the following probabilities.a. P(0 z.83)b. P(1.57 z0)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(z 2.5)e. P(3 z 0)
10. Draw a graph for the standard normal distribution. Label the horizontal axis at values of 3, 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
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. On average, 30-minute television sitcoms have 22 minutes of programming (CNBC, February 23, 2006). Assume that the probability distribution for minutes of programming can be approximated by a uniform distribution from 18 minutes to 26 minutes.a. What is the probability a sitcom will have 25 or
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 x18).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 x1.25).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 (http://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. A new 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 (http://www.zogby.com, January 12, 2004). Suppose a sample of 800 people who
59. The unemployment rate in the state of Arizona is 4.1% (http://money.cnn.com, May 2, 2007). Assume that 100 employable people in Arizona 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
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(http://www.bts.gov, January 12, 2004).a.
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