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Basic Business Statistics Concepts And Applications 12th Edition Mark L. Berenson, David M. Levine, Timothy C. Krehbiel - Solutions

A study of the time spent shopping in a supermarket for a market basket of 20 specific items showed an approximately uniform distribution between 20 minutes and 40 minutes. What is the probability that the shopping time will be1. Between 25 and 30 minutes?2. Less than 35 minutes?3. Determine the
How long does it take you to download a game for your iPod? According to Apple's technical support site, www.apple.com/support/itunes, downloading an iPod game using a broadband connection should take 3 to 6 minutes. Assume that the download times are uniformly distributed between 3 and 6 minutes.
The scheduled commuting time on the Long Island Railroad from Glen Cove to New York City is 65 minutes. Suppose that the actual commuting time is uniformly distributed between 64 and 74 minutes. What is the probability that the commuting time will be1. Less than 70 minutes?2. Between 65 and 70
Given an exponential distribution with λ = 10, what is the probability that the arrival time isa. Less than X = 0.1?b. Greater than X = 0.1?c. Between X = 0.1 and X = 0.2?d. Less than X = 0.1 or greater than X = 0.2?
Given an exponential distribution with λ = 30, what is the probability that the arrival time isa. Less than X = 0.1?b. Greater than X = 0.1?c. Between X = 0.1 and X = 0.2?d. Less than X = 0.1or greater than X = 0.2?
Given a standardized normal distribution (with a mean of 0 and a standard deviation of 1, as in Table E.2), what is the probability thata. Z is less than 1.08?b. Z is greater than - 0.21?c. Z is less than - 0.21 or greater than the mean?d. Z is less than - 0.21 or greater than 1.08?
Given an exponential distribution with λ = 5, what is the probability that the arrival time isa. Less than X = 0.3b. Greater than X = 0.3?c. Between X = 0.3 and X = 0.5?d. Less than X = 0.3 or greater than X = 0.5?
Autos arrive at a toll plaza located at the entrance to a bridge at a rate of 50 per minute during the 5:00-to-6:00 P.M. hour. If an auto has just arrived,a. What is the probability that the next auto will arrive within 3 seconds (0.05 minute)?b. What is the probability that the next auto will
Customers arrive at the drive-up window of a fast-food restaurant at a rate of 2 per minute during the lunch hour.a. What is the probability that the next customer will arrive within 1 minute?b. What is the probability that the next customer will arrive within 5 minutes?c. During the dinner time
Telephone calls arrive at the information desk of a large computer software company at a rate of 15 per hour.a. What is the probability that the next call will arrive within 3 minutes (0.05 hour)?b. What is the probability that the next call will arrive within 15 minutes (0.25 hour)?c. Suppose the
An on-the-job injury occurs once every 10 days on average at an automobile plant. What is the probability that the next on-the-job injury will occur withina. 10 days?b. 5 days?c. 1 day?
The time between unplanned shutdowns of a power plant has an exponential distribution with a mean of 20 days. Determine the probability that the time between two unplanned shutdowns is1. Less than 14 days.2. More than 21 days.3. Less than 7 days.
Golfers arrive at the starter's booth of a public golf course at a rate of 8 per hour during the Monday-to-Friday midweek period. If a golfer has just arrived,a. What is the probability that the next golfer will arrive within 15 minutes (0.25 hour)?b. What is the probability that the next golfer
Some Internet companies sell a service that will boost a website's traffic by delivering additional unique visitors. Assume that one such company claims it can deliver 1,000 visitors a day. If this amount of website traffic is experienced, then the time between visitors has a mean of 1.44 minutes
Given a standardized normal distribution (with a mean of 0 and a standard deviation of 1, as in Table E.2), determine the following probabilities:a. P(Z > 1.08)b. P(Z < - 0.21)c. P(- 1.96 < Z < - 0.21)d. What is the value of Z if only 15.87% of all possible Z values are larger?
What are some of the distinguishing properties of a normal distribution? Discuss.
How does the shape of the normal distribution differ from the shapes of the uniform and exponential distributions? Discuss.
An industrial sewing machine uses ball bearings that are targeted to have a diameter of 0.75 inch. The lower and upper specification limits under which the ball bearings can operate are 0.74 inch and 0.76 inch, respectively. Past experience has indicated that the actual diameter of the ball
The fill amount in 2-liter soft drink bottles is normally distributed, with a mean of 2.0 liters and a standard deviation of 0.05 liter. If bottles contain less than 95% of the listed net content (1.90 liters, in this case), the manufacturer may be subject to penalty by the state office of consumer
In an effort to reduce the number of bottles that contain less than 1.90 liters, the bottler in Problem 6.46 sets the filling machine so that the mean is 2.02 liters. Under these circumstances, what are your answers in Problem 6.46 (a) through (e)?
An orange juice producer buys all his oranges from a large orange grove. The amount of juice squeezed from each of these oranges is approximately normally distributed, with a mean of 4.70 ounces and a standard deviation of 0.40 ounce.a. What is the probability that a randomly selected orange will
The file DemesticBeer contains the percentage alcohol, number of calories per 12 ounces, and number of carbohydrates (in grams) per 12 ounces for 139 of the best-selling domestic beers in the United States. For each of the three variables, decide whether the data appear to be approximately normally
Given a normal distribution with μ = 100 and σ = 10, what is the probability thata. X > 75?b. X < 70?c. X < 80 or X > 110?d. Between what two X values (symmetrically distributed around the mean) are 80% of the values?
The evening manager of a restaurant was very concerned about the length of time some customers were waiting in line to be seated. She also had some concern about the seating times-that is, the length of time between when a customer is seated and the time he or she leaves the restaurant. Over the
All the major stock market indexes posted strong gains in 2009. The mean one-year return for stocks in the S&P 500, a group of 500 very large companies, was 23.45%. The mean one-year return for the NASDAQ, a group of 3,200 small and medium-sized companies, was 43.89%. Historically, the one-year
The speed in which the home page of a website is downloaded is an important quality characteristic of that website. Suppose that the mean time to download the home page for the Internal Revenue Service is 1.2 seconds. Suppose that the download time is normally distributed, with a standard deviation
Suppose that the mean download time for a commercial tax preparation site is 2.0 seconds. Suppose that the download time is normally distributed, with a standard deviation of 0.5 second. What is the probability that a download time isa. Less than 2 seconds?b. Between 1.5 and 2.5 seconds?c. Above
For the expense ratio, three-year return, and five-year return, decide whether the data are approximately normally distributed bya. Comparing data characteristics to theoretical properties.b. Constructing a normal probability plot.
Problem 1.27 on page 14 describes a survey of 62 undergraduate students (stored in ). For these data, for each numerical variable, decide whether the data are approximately normally distributed bya. Comparing data characteristics to theoretical properties.b. Constructing a normal probability
Problem 1.28 on page 15 describes a survey of 44 MBA students (stored in GradSurvey). For these data, for each numerical variable, decide whether the data are approximately normally distributed by a. Comparing data characteristics to theoretical properties. b. Constructing a normal probability
Given a normal distribution with μ = 50 and σ = 4, what is the probability thata. X > 43?b. X < 42?c. 5% of the values are less than what X value?d. Between what two X values (symmetrically distributed around the mean) are 60% of the values?
In 2008, the per capita consumption of coffee in the United States was reported to be 4.2 kg, or 9.24 pounds (data extracted from en.wikipedia.org/wiki/List_of_countries_ by_coffee_consumption_per_capita). Assume that the per capita consumption of coffee in the United States is approximately
Toby's Trucking Company determined that the distance traveled per truck per year is normally distributed, with a mean of 50 thousand miles and a standard deviation of 12 thousand miles.1. What proportion of trucks can be expected to travel between 34 and 50 thousand miles in a year?2. What
Consumers spend an average of $21 per week in cash without being aware of where it goes (data extracted from "Snapshots: A Hole in Our Pockets," USA Today, January 18, 2010, p. 1A). Assume that the amount of cash spent without being aware of where it goes is normally distributed and that the
A survey indicates that the vast majority of college students own their own personal computers. What information would you want to know before you accepted the results of this survey? Discuss.
A simple random sample of n = 300 full-time employees is selected from a company list containing the names of all N = 5,000 full-time employees in order to evaluate job satisfaction. a. Give an example of possible coverage error. b. Give an example of possible nonresponse error. c. Give an example
Business Professor Thomas Callarman traveled to China more than a dozen times from 2000 to 2005. He warns people about believing everything they read about surveys conducted in China and gives two specific reasons: "First, things are changing so rapidly that what you hear today may not be true
A recent survey of college freshmen investigated the amount of involvement their parents have with decisions concerning their education. When asked about the decision to go to college, 84% said their parents' involvement was about right, 10.3% said it was too much, and 5.7% said it was too little.
Recruiters are finding a wealth of unfiltered information about candidates on social-networking websites. A recent survey found that 83% of recruiters use search engines to learn more about candidates, and 43% eliminated candidates based on information they found (I. Phaneuf, "Who's Googling You?"
Given a normal distribution with μ = 100 and σ = 10, if you select a sample of n = 25, what is the probability that isa. Less than 95?b. Between 95 and 97.5?c. Above 102.2?d. There is a 65% chance that is above what value?
Given a normal distribution with μ = 50 and σ = 5, if you select a sample of n = 100, what is the probability that isa. Less than 47?b. Between 47 and 49.5?c. Above 51.1?d. There is a 35% chance that is above what value?
For each of the following three populations, indicate what the sampling distribution for samples of 25 would consist of: a. Travel expense vouchers for a university in an academic year b. Absentee records (days absent per year) in 2010 for employees of a large manufacturing company. c. Yearly sales
The following data represent the number of days absent per year in a population of six employees of a small company:a. Assuming that you sample without replacement, select all possible samples of n = 2and construct the sampling distribution of the mean. Compute the mean of all the sample means and
The diameter of a brand of Ping-Pong balls is approximately normally distributed, with a mean of 1.30 inches and a standard deviation of 0.04 inch. If you select a random sample of 16 Ping-Pong balls,a. What is the sampling distribution of the mean?b. What is the probability that the sample mean is
For a population of N = 902, verify that by starting in row 05, column 01 of the table of random numbers (Table E.1), you need only six rows to select a sample of N = 60 without replacement.
The U.S. Census Bureau announced that the median sales price of new houses sold in 2009 was $215,600, and the mean sales price was $270,100 (www.census.gov/ newhomesales, March 30, 2010). Assume that the standard deviation of the prices is $90,000.a. If you select samples of n = 2, describe the
Time spent using e-mail per session is normally distributed, with μ = 8 minutes and σ = 2 minutes. If you select a random sample of 25 sessions,a. what is the probability that the sample mean is between 7.8 and 8.2 minutes?b. what is the probability that the sample mean is between 7.5 and 8
The amount of time a bank teller spends with each customer has a population mean, μ = 3.10 minutes and a standard deviation, σ = 0.40 minute. If you select a random sample of 16 customers,a. What is the probability that the mean time spent per customer is at least 3 minutes?b. There is an 85%
A political pollster is conducting an analysis of sample results in order to make predictions on election night. Assuming a two-candidate election, if a specific candidate receives at least 55% of the vote in the sample, that candidate will be forecast as the winner of the election. If you select a
You plan to conduct a marketing experiment in which students are to taste one of two different brands of soft drink. Their task is to correctly identify the brand tasted. You select a random sample of 200 students and assume that the students have no ability to distinguish between the two brands.a.
In a recent survey of full-time female workers ages 22 to 35 years, 46% said that they would rather give up some of their salary for more personal time. (Data extracted from "I'd Rather Give Up," USA Today, March 4, 2010, p. 1B.) Suppose you select a sample of 100 full-time female workers 22 to 35
Companies often make flextime scheduling available to help recruit and keep female employees who have children. Other workers sometimes view these flextime schedules as unfair. An article in USA Today indicates that 25% of male employees state that they have to pick up the slack for moms working
Given a population of N = 93, starting in row 29, column 01 of the table of random numbers (Table E.1), and reading across the row, select a sample of N = 15 a. Without replacement. b. With replacement.
According to Gallup's poll on consumer behavior, 36% of Americans say they will consider only cars manufactured by an American company when purchasing a new car. (Data extracted from The Gallup Poll, www.gallup.com, March 31, 2010.) If you select a random sample of 200 Americans,a. What is the
The Agency for Healthcare Research and Quality reports that medical errors are responsible for injury to 1 out of every 25 hospital patients in the United States. (Data extracted from M. Ozan-Rafferty, "Hospitals: Never Have a Never Event," The Gallup Management Journal, gmj. gallup.com, May 7,
A survey of 2,250 American adults reported that 59% got news both online and offline in a typical day. (Data extracted from "How Americans Get News in a Typical Day," USA Today, March 10, 2010, p. 1A.)1. Suppose that you take a sample of 100 American adults. If the population proportion of American
Why does the standard error of the mean decrease as the sample size, n, increases? Discuss.
Why does the sampling distribution of the mean follow a normal distribution for a large enough sample size, even though the population may not be normally distributed? Discuss.
What is the difference between probability sampling and nonprobability sampling?
What is the difference between sampling with replacement versus sampling without replacement?
What is the difference between a simple random sample and a systematic sample?
What is the difference between a simple random sample and a stratified sample?
What is the difference between a stratified sample and a cluster sample?
An industrial sewing machine uses ball bearings that are targeted to have a diameter of 0.75 inch. The lower and upper specification limits under which the ball bearing can operate are 0.74 inch (lower) and 0.76 inch (upper). Past experience has indicated that the actual diameter of the ball
The fill amount of bottles of a soft drink is normally distributed, with a mean of 2.0 liters and a standard deviation of 0.05 liter. If you select a random sample of 25 bottles, what is the probability that the sample mean will be1. Between 1.99 and 2.0 liters?2. Below 1.98 liters?3. Greater than
An orange juice producer buys oranges from a large orange grove that has one variety of orange. The amount of juice squeezed from these oranges is approximately normally distributed, with a mean of 4.70 ounces and a standard deviation of 0.40 ounce. Suppose that you select a sample of 25 oranges.a.
In Problem 7.46, suppose that the mean amount of juice squeezed is 5.0 ounces.a. What is the probability that the sample mean amount of juice will be at least 4.60 ounces?b. The probability is 70% that the sample mean amount of juice will be contained between what two values symmetrically
Junk bonds reported strong returns in 2009. The population of junk bonds earned a mean return of 57.5% in 2009. (Data extracted from The Wall Street Journal, January 4, 2010, p. R1.) Assume that the returns for junk bonds were distributed as a normal random variable, with a mean of 57.5 and a
The article mentioned in Problem 7.48 reported that Treasury bonds had a mean return of -9.3% in 2009. Assume that the returns for the Treasury bonds were distributed as a normal random variable, with a mean of -9.3 and a standard deviation of 10. If you select an individual Treasury bond from this
A population has four members (called A, B, C, and D). You would like to select a random sample of n = 2, which you decide to do in the following way: Flip a coin; if it is heads, the sample will be items A and B; if it is tails, the sample will be items C and D. Although this is a random sample,
The registrar of a college with a population of N = 4,000 full-time students is asked by the president to conduct a survey to measure satisfaction with the quality of life on campus.The following table contains a breakdown of the 4,000 registered full-time students, by gender and class
Prenumbered sales invoices are kept in a sales journal. The invoices are numbered from 0001 to 5000. a. Beginning in row 16, column 01, and proceeding horizontally in Table E.1, select a simple random sample of 50 invoice numbers. b. Select a systematic sample of 50 invoice numbers. Use the random
Suppose that 5,000 sales invoices are separated into four strata. Stratum 1 contains 50 invoices, stratum 2 contains 500 invoices, stratum 3 contains 1,000 invoices, and stratum 4 contains 3,450 invoices. A sample of 500 sales invoices is needed.a. What type of sampling should you do? Why?b.
The quality control manager at a light bulb factory needs to estimate the mean life of a large shipment of light bulbs. The standard deviation is 100 hours. A random sample of 64 light bulbs indicated a sample mean life of 350 hours.a. Construct a 95% confidence interval estimate for the population
Determine the critical value of t in each of the following circumstances:a. 1 - α = 0.95, n = 10b. 1 - α = 0.99, n = 10c. 1 - α = 0.95, n = 32d. 1 - α = 0.95, n = 65e. 1 - α = 0.90, n = 16
Assuming that the population is normally distributed, construct a 95% confidence interval estimate for the population mean for each of the following samples:Explain why these two samples produce different confidence intervals even though they have the same mean and range.
Assuming that the population is normally distributed, construct a 95% confidence interval for the population mean, based on the following sample of size n = 7:1, 2, 3, 4, 5, 6, 20Change the number 20 to 7 and recalculate the confidence interval. Using these results, describe the effect of an
A stationery store wants to estimate the mean retail value of greeting cards that it has in its inventory. A random sample of 100 greeting cards indicates a mean value of $2.55 and a standard deviation of $0.44.i. Assuming a normal distribution, construct a 95% confidence interval estimate for the
Southside Hospital in Bay Shore, NewYork, commonly conducts stress tests to study the heart muscle after a person has a heart attack. Members of the diagnostic imaging department conducted a quality improvement project with the objective of reducing the turnaround time for stress tests. Turnaround
The U.S. Department of Transportation requires tire manufacturers to provide tire performance information on the sidewall of a tire to better inform prospective customers as they make purchasing decisions. One very important measure of tire performance is the tread wear index, which indicates the
The file contains the amount that a sample of nine customers spent for lunch ($) at a fast-food restaurant4.20 5.03 5.86 6.45 7.38 7.54 8.46 8.47 9.87a. Construct a 95% confidence interval estimate for the population mean amount spent for lunch ($) at a fast-food restaurant, assuming a normal
The file Sedans contains the overall miles per gallon (MPG) of 2010 family sedans.a. Construct a 95% confidence interval estimate for the population mean MPG of 2010 family sedans, assuming a normal distribution. b. Interpret the interval constructed in (a). c. Compare the results in (a) to those
The file SUV contains the overall miles per gallon (MPG) of 2010 small SUVs.a. Construct a 95% confidence interval estimate for the population mean MPG of 2010 small SUVs, assuming a normal distribution.b. Interpret the interval constructed in (a).c. Compare the results in (a) to those in Problem
Is there a difference in the yields of different types of investments? The file SavingsRate-MMCD contains the yields for a money market account and a five-year certificate of deposit (CD) for 25 banks in the United States, as of March 29, 2010.a. Construct a 95% confidence interval estimate for the
One of the major measures of the quality of service provided by any organization is the speed with which it responds to customer complaints. A large family-held department store selling furniture and flooring, including carpet, had undergone a major expansion in the past several years. In
In NewYork State, savings banks are permitted to sell a form of life insurance called savings bank life insurance (SBLI). The approval process consists of underwriting, which includes a review of the application, a medical information bureau check, possible requests for additional medical
The file DarkChocolate contains the cost per ounce ($) for a sample of 14 dark chocolate bars:a. Construct a 95% confidence interval estimate for the population cost per ounce ($) of dark chocolate bars.b. What assumption do you need to make about the population distribution to construct the
One operation of a mill is to cut pieces of steel into parts that are used in the frame for front seats in an automobile. The steel is cut with a diamond saw, and the resulting parts must be cut to be within ± 0.005 inch of the length specified by the automobile company. The measurement reported
If n = 200 and X = 50, construct a 95% confidence interval estimate for the population proportion.
If n = 400 and X = 25, construct a 99% confidence interval estimate for the population proportion.
The telephone company has the business objective of wanting to estimate the proportion of households that would purchase an additional telephone line if it were made available at a substantially reduced installation cost. Data are collected from a random sample of 500 households. The results
In a survey of 1,200 social media users, 76% said it is okay to friend co-workers, but 56% said it is not okay to friend your boss. (Data extracted from "Facebook Etiquette at Work," USA Today, March 24, 2010, p. 1B.)a. Construct a 95% confidence interval estimate for the population proportion of
Why is it not possible in Example 8.1 on page 284 to have 100% confidence? Explain.
Have you ever negotiated a pay raise? According to an Accenture survey, 52% of U.S. workers have (J.Yang and K. Carter, "HaveYou Ever Negotiated a Pay Raise?" www. usatoday.com, May 22, 2009).a. Suppose that the survey had a sample size of Construct a 95% confidence interval for the proportion of
In a survey of 1,000 airline travelers, 760 responded that the airline fee that is most unreasonable is additional charges to redeem points/miles. (Data extracted from "Which Airline Fee Is Most Unreasonable?" USA Today, December 2, 2008, p. B1.) Construct a 95% confidence interval estimate for the
In a survey of 2,395 adults, 1,916 reported that e-mails are easy to misinterpret, but only 1,269 reported that telephone conversations are easy to misinterpret. (Data extracted from "Open to Misinterpretation," USA Today, July 17, 2007, p. 1D.)a. Construct a 95% confidence interval estimate for
What are the most preferred forms of recognition in the workplace? In a survey by Office Arrow, 163 of 388 administrative professionals responded that verbal recognition is the most preferred form of recognition, and 74 responded that cash bonuses are most preferred. (Data extracted from "Most
A survey is planned to determine the mean annual family medical expenses of employees of a large company. The management of the company wishes to be 95% confident that the sample mean is correct to within ± $50 of the population mean annual family medical expenses. A previous study indicates that
A consumer group wants to estimate the mean electric bill for the month of July for single-family homes in a large city. Based on studies conducted in other cities, the standard deviation is assumed to be $25. The group wants to estimate, with 99% confidence, the mean bill for July to within ±
An advertising agency that serves a major radio station wants to estimate the mean amount of time that the station's audience spends listening to the radio daily. From past studies, the standard deviation is estimated as 45 minutes.a. What sample size is needed if the agency wants to be 90%

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