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essentials of statistics

Questions and Answers of Essentials Of Statistics

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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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.
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
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
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
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
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
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
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
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
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
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
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,
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
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
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
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
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
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
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
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.
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
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
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,
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
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
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
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
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.
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
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
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
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
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
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
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
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
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
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
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.
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
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
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,
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
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
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
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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

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