How do the empirical rule and the Chebyshev rule differ?
> According to the same Glassdoor source mentioned in Problem 6.40, the mean monthly pay for interns at Facebook is $6,589. Suppose that the intern monthly pay is normally distributed, with a standard deviation of $500. What is the probability that the mon
> Interns report that when deciding on where to work, career growth, salary and compensation, location and commute, and company culture and values are important factors to them. According to reports by interns to Glassdoor, the mean monthly pay of interns
> 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 subje
> Given a normal distribution with m = 100 and s = 10, what is the probability that a. X > 75? b. X < 70? c. X < 80 or X > 110? d. Between what two X values (symmetrically distributed around the mean) are 80 percent of the values?
> 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
> How can you use the normal probability plot to evaluate whether a set of data is normally distributed?
> The file CDRate contains the yields for one-year certificates of deposit (CDs) and for five-year CDs for 39 banks in the United States, as of January 9, 2017. Source: Data extracted and compiled from www.bankrate.com, January 9, 2017. a. Construct a ste
> How does the shape of the normal distribution differ from the shapes of the uniform and exponential distributions?
> The major stock market indexes had strong results in 2016. The mean one-year return for stocks in the S&P 500, a group of 500 very large companies, was +9.54%. The mean one-year return for Chapter Review Problems 245 246 CHAPTER 6 | The Normal Distributi
> For each of the following, indicate whether the type of probability involved is an example of a priori probability, empirical probability, or subjective probability. a. The next toss of a fair coin will land on heads. b. Italy will win soccer’s World Cup
> The following data represent the number of days absent per year in a population of six employees of a small company: 1 3 6 7 9 10 a. Assuming that you sample without replacement, select all possible samples of n = 2 and construct the sampling distributi
> What are some of the distinguishing properties of a normal distribution?
> How do you find the X value that corresponds to a given percentile of the normal distribution?
> How do you find the area between two values under the normal curve?
> 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 be a.
> 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 percent of a
> How long does it take to download a two-hour HD movie from the iTunes store? According to Apple’s technical support site, support.apple.com/en-us/HT201587, downloading such a movie using a 15 Mbit/s broadband connection should take 29–43 minutes. Assume
> Nielsen study indicates that 18- to 34-year olds spend a mean of 93 minutes watching video on their smartphones per week. Source: Data extracted from bit.ly/2rj8GHm. Assume that the amount of time watching video on a smartphone per week is normally dist
> 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 be a. between 25 and 30 minut
> The time between arrivals of customers at a bank during the noon-to-1 P.M. hour has a uniform distribution between 0 to 120 seconds. What is the probability that the time between the arrival of two customers will be a. less than 20 seconds? b. between 10
> Suppose you select one value from a uniform distribution with a = 0 and b = 10. What is the probability that the value will be a. between 5 and 7? b. between 2 and 3? c. What is the mean? d. What is the standard deviation?
> The file Utility contains the electricity costs, in dollars, during July of a recent year for a random sample of 50 one-bedroom apartments in a large city: 96 171 202 178 147 102 153 197 127 82 157 185 90 116 172 111 148 213 130 165 141 149 206 175 1
> Consider the following contingency table: What is the probability of event a. A? b. A and B? c. A and B? d. A or B? в B' A 10 30 A' 25 35
> The file CD Rate contains the yields for a one-year certificate of deposit (CD) and a five-year CD for 39 banks listed for West Palm Beach, Florida on January 9, 2017. Source: Data extracted from www.Bankrate.com, January 9, 2017. For each type of inves
> A lock on a bank vault consists of three dials, each with 30 positions. In order for the vault to open, each of the three dials must be in the correct position. a. How many different possible dial combinations are there for this lock? b. What is the pr
> One operation of a mill is to cut pieces of steel into parts that will later be used as the frame for front seats in an automotive plant. The steel is cut with a diamond saw, and the resulting parts must be within {0.005 inch of the length specified by t
> Thirty companies comprise the DJIA. How big are these companies? One common method for measuring the size of a company is to use its market capitalization, which is computed by multiplying the number of stock shares by the price of a share of stock. On J
> An urn contains 12 red balls and 8 white balls. One ball is to be selected from the urn. a. Give an example of a simple event. b. What is the complement of a red ball? c. What does the sample space consist of?
> The file CigaretteTax contains the state cigarette tax ($) for each state and the District of Columbia as of January 1, 2017. a. Construct an ordered array. b. Plot a percentage histogram. c. What conclusions can you reach about the differences in the
> 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 that a. 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 th
> 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 that a. Z is between -1.57 and 1.84? b. Z is less than -1.57 or greater than 1.84? c. What is the value of Z if only 2.5 p
> 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 that a. Z is less than 1.57? b. Z is greater than 1.84? c. Z is between 1.57 and 1.84? d. Z is less than 1.57 or greater t
> The file DomesticBeer contains the percentage alcohol, number of calories per 12 ounces, and number of carbohydrates (in grams) per 12 ounces for 158 of the best-selling domestic beers in the United States. Determine whether each of these variables appea
> Refer to Problem 5.40. In the same time period, 24% of the consumers registering a bank account and service compliant cited “deposit and withdrawal” as the type of complaint; these are issues such as transaction holds and unauthorized transactions. a. W
> The Consumer Financial Protection Bureau’s Consumer Response Team hears directly from consumers about the challenges they face in the marketplace, brings their concerns to the attention of financial institutions, and assists in addressing their complaint
> Social log-ins involve recommending or sharing an article that you read online. According to Janrain, in the first quarter of 2017, 45% signed in via Facebook compared with 26% for Google. Source: Jainrain.com blog, “Identity and social login trends acr
> Refer to Problem 5.37. Suppose that a quality improvement initiative has reduced the percentage of medical bills containing errors to 40%. If a sample of 10 medical bills is selected, what is the probability that a. 0 medical bills will contain errors?
> Medical billing errors and fraud are on the rise. According to Medical Billing Advocates of America, three out of four times, the medical bills that they review contain errors. Source: Kelly Gooch, “Medical billing errors growing, says Medical Billing A
> The file Property Taxes contains the property taxes on a $176K home for the 50 states and the District of Columbia. Decide whether the data appear to be approximately normally distributed by a. comparing data characteristics to theoretical properties.
> The file DomesticBeer contains the percentage alcohol, number of calories per 12 ounces, and number of carbohydrates (in grams) per 12 ounces for 158 of the best selling domestic beers in the United States. Source: Data extracted from www.beer100.com/bee
> 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
> One of the major measures of the quality of service provided by an 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 expan
> An insurance company has the business objective of reducing the amount of time it takes to approve applications for life insurance. The approval process consists of underwriting, which includes a review of the application, a medical information bureau ch
> The American Society for Quality (ASQ) conducted a salary survey of all its members. ASQ members work in all areas of manufacturing and service-related institutions, with a common theme of an interest in quality. Manager and quality engineer were the mos
> How do the covariance and the coefficient of correlation differ?
> 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. Supp
> What is the difference between the arithmetic mean and the geometric mean?
> What is the difference between skewness and kurtosis?
> What is meant by the property of shape?
> How does the empirical rule help explain the ways in which the values in a set of numerical data cluster and distribute?
> What are the differences among the various measures of variation, such as the range, interquartile range, variance, standard deviation, and coefficient of variation, and what are the advantages and disadvantages of each?
> What does the Z score measure?
> What is meant by the property of variation?
> How do you interpret the first quartile, median, and third quartile?
> What are the differences among the mean, median, and mode, and what are the advantages and disadvantages of each?
> 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 be a. between 1.99 and 2.
> What is meant by the property of central tendency?
> Movie companies need to predict the gross receipts of individual movies once a movie has debuted. The following results, stored in PotterMovies , are the first weekend gross, the U.S. gross, and the worldwide gross (in $millions) of the eight Harry Potte
> A Pew Research Center survey found a noticeable rise in smartphone ownership and internet usage in emerging and developing nations, and once online, adults in these nations are hungry for social interaction. The file GlobalInternetUsage contains the leve
> The file MobileSpeed contains the overall download and upload speeds in mbps for nine carriers in the U.S. Source: Data extracted from “Best Mobile Network 2016,” bit.ly/1KGPrMm, accessed November 10, 2016. a. Compute the covariance between download spee
> Movie companies need to predict the gross receipts of individual movies once a movie has debuted. The data, shown below and stored in PotterMovies , are the first weekend gross, the U.S. gross, and the worldwide gross (in $ millions) of the eight Harry P
> The file Cereals lists the calories and sugar, in grams, in one serving of seven breakfast cereals: a. Compute the covariance. b. Compute the coefficient of correlation. c. Which do you think is more valuable in expressing the relationship between calo
> A study of 267 college students investigated the impact of smartphones on student connectedness and out-of-class involvement. Source: Liu X, et al., “The Impact of Smartphone Educational Use on Student Connectedness and Out-of-Class Involvement,” The Ele
> The following is a set of data from a sample of n = 11 items: X 7 5 8 3 6 10 12 4 9 15 18 Y 21 15 24 9 18 30 36 12 27 45 54 a. Compute the covariance. b. Compute the coefficient of correlation. c. How strong is the relationship between X and Y? Explain.
> Thirty companies comprise the DJIA. Just how big are these companies? One common method for measuring the size of a company is to use its market capitalization, which is computed by multiplying the number of stock shares by the price of a share of stock.
> The file Energy contains the average residential price for electricity in cents per kilowatt hour in each of the 50 states and the District of Columbia during a recent year. a. Compute the mean, variance, and standard deviation for the population. b. Wha
> 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 indicate
> The file CigaretteTax contains the state cigarette tax (in $) for each of the 50 states and the District of Columbia as of January 1, 2017. a. Compute the population mean and population standard deviation for the state cigarette tax. b. Interpret the par
> Consider a population of 1,024 mutual funds that primarily invest in large companies. You have determined that m, the mean one-year total percentage return achieved by all the funds, is 8.20 and that s, the standard deviation, is 2.75. a. According to th
> The following is a set of data for a population with N = 10: 7 5 6 6 6 4 8 6 9 3 a. Compute the population mean. b. Compute the population standard deviation.
> The following is a set of data for a population with N = 10: 7 5 11 8 3 6 2 1 9 8 a. Compute the population mean. b. Compute the population standard deviation.
> A bank branch located in a commercial district of a city has the business objective of developing an improved process for serving customers during the noon-to-1:00 p.m. lunch period. The waiting time, in minutes, is defined as the time the customer enter
> The file CD Rate contains the yields for one-year CDs and five-year CDs, for 39 banks in the United States, as of January 9, 2017. Source: Data extracted from www.Bankrate.com, January 9, 2017. For each type of account: a. Compute the first quartile (Q1)
> The annual NFL Super Bowl is the most widely watched sporting event in the United States each year. In recent years, there has been a great deal of interest in the ads that appear during the game. These ads vary in length with most lasting 30 seconds or
> The file HotelAway contains the average room price (in US$) paid by various nationalities while traveling abroad (away from their home country) in 2016: 124 101 115 126 114 112 138 85 138 96 130 116 Source: Data extracted from hpi.hotels.com/. a. Compute
> The file MobileCommerce contains the following mobile commerce penetration values, the percentage of the country population that bought something online via a mobile phone in the past month, for twenty-eight of the world’s economies: 23 27 26 25 40 19 26
> The file AccountingPartners contains the number of partners in a cohort of rising accounting firms that have been tagged as “firms to watch.” The firms have the following number of partners: 37 41 26 14 22 29 36 11 16 29 30 20 20 20 26 21 17 21 14 28 24
> Under what circumstances does the sampling distribution of the proportion approximately follow the normal distribution?
> The following is a set of data from a sample of n = 5: 7 -5 -8 7 9 a. Compute the first quartile (Q1), the third quartile (Q3), and the interquartile range. b. List the five-number summary. c. Construct a boxplot and describe its shape. d. Compare your a
> The following is a set of data from a sample of n = 5: 7 4 9 8 2 a. Compute the first quartile (Q1), the third quartile (Q3), and the interquartile range. b. List the five-number summary. c. Construct a boxplot and describe its shape. d. Compare your ans
> The following is a set of data from a sample of n = 6: 7 4 9 7 3 12 a. Compute the first quartile (Q1), the third quartile (Q3), and the interquartile range. b. List the five-number summary. c. Construct a boxplot and describe its shape. d. Compare your
> The following is a set of data from a sample of n = 7: 12 7 4 9 0 7 3 a. Compute the first quartile (Q1), the third quartile (Q3), and the interquartile range. b. List the five-number summary. c. Construct a boxplot and describe its shape. d. Compare you
> Using the three-year return percentage variable in Retirement Funds: a. Construct a table that computes the mean for each combination of type, risk, and rating. b. Construct a table that computes the standard deviation for each combination of type, ris
> Using the three-year return percentage variable in Retirement Funds: a. Construct a table that computes the mean for each combination of market cap, risk, and rating. b. Construct a table that computes the standard deviation for each combination of mar
> Using the three-year return percentage variable in Retirement Funds: a. Construct a table that computes the mean for each combination of type, market cap, and rating. b. Construct a table that computes the standard deviation for each combination of typ
> Using the three-year return percentage variable in Retirement Funds: a. Construct a table that computes the mean for each combination of type, market cap, and risk. b. Construct a table that computes the standard deviation for each combination of type,
> In 2013 through 2016, the value of precious metals fluctuated dramatically. The following data (stored in Metals ) represent the total rate of return (in percentage) for platinum, gold, and silver from 2013 through 2016: a. Compute the geometric mean r
> The file Indices contains the total rate of return percentage for the Dow Jones Industrial Average (DJIA), the Standard & Poor’s 500 (S&P 500), and the technology-heavy NASDAQ Composite (NASDAQ) from 2013 through 2016. These dat
> What is the difference between a population distribution and a sampling distribution?
> Facebook’s stock price in 2015 increased by 34.15%, and in 2016, it increased by 9.93%. Source: Data extracted from finance.yahoo.com, January 9, 2017. a. Compute the geometric mean rate of return per year for the twoyear period 2015–2016. b. If you purc
> General Electric (GE) is one of the world’s largest companies; it develops, manufactures, and markets a wide range of products, including medical diagnostic imaging devices, jet engines, lighting products, and chemicals. In 2015, the stock price rose 23.
> Suppose that another bank branch, located in a residential area, is also concerned with the noon-to-1:00 p.m. lunch hour. The waiting time, in minutes, collected from a sample of 15 customers during this hour, are stored in Bank2 : 9.66 5.90 8.02 5.79 8.
> A bank branch located in a commercial district of a city has the business objective of developing an improved process for serving customers during the noon-to-1:00 p.m. lunch period. The waiting time, in minutes, is defined as the time the customer enter
> The file HotelAway contains the average room price (in US$) paid by various nationalities while traveling abroad (away from their home country) in 2016: 124 101 115 126 114 112 138 85 138 96 130 116 132 Source: Data extracted from hpi.hotels.com/. a. Com
> Is there a difference in the variation of the yields of different types of investments? The file CD Rate contains the yields for oneyear certificates of deposit (CDs) and five-year CDs for 39 banks listed for West Palm Beach, Florida on January 9, 2017.
> The file MobileCommerce contains the following mobile commerce penetration values, the percentage of the country population that bought something online via a mobile phone in the past month, for 28 of the world’s economies: 23 27 26 25 40 19 26 36 23 33
> The file AccountingPartners contains the number of partners in a cohort of rising accounting firms that have been tagged as “firms to watch.” The firms have the following numbers of partners: 37 41 26 14 22 29 36 11 16 29 30 20 20 20 26 21 17 21 14 28 24
> The annual NFL Super Bowl is the most widely watched sporting event in the United States each year. In recent years, there has been a great deal of interest in the ads that appear during the game. These ads vary in length with most lasting 30 seconds or
> The file AirportRating contains the rating of large and medium size airports in the United States and Canada. Source: Data extracted from N. Trejos, “Portland, Indianapolis Top Airport Rankings, USA Today, December 16, 2016, p. 4B. For large and medium
> 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?
