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 Distribution and Other Continuous Distributions the NASDAQ, a group of 3,200 small and medium-sized companies, was +7.50%. Historically, the one-year returns are approximately normally distributed, the standard deviation in the S&P 500 is approximately 20%, and the standard deviation in the NASDAQ is approximately 30%. a. What is the probability that a stock in the S&P 500 gained value in 2016? b. What is the probability that a stock in the S&P 500 gained 10% or more in 2016? c. What is the probability that a stock in the S&P 500 lost 20% or more in 2016? d. What is the probability that a stock in the S&P 500 lost 30% or more in 2016? e. Repeat (a) through (d) for a stock in the NASDAQ. f. Write a short summary on your findings. Be sure to include a discussion of the risks associated with a large standard deviation.
> A quality characteristic of interest for a tea-bag-filling process is the weight of the tea in the individual bags. If the bags are underfilled, two problems arise. First, customers may not be able to brew the tea to be as strong as they wish. Second, th
> The diameter of a brand of tennis balls is approximately normally distributed, with a mean of 2.63 inches and a standard deviation of 0.03 inch. If you select a random sample of nine tennis balls, a. what is the sampling distribution of the mean? b. wh
> Data were collected on the typical cost of dining at Americancuisine restaurants within a 1-mile walking distance of a hotel located in a large city. The file Bundle contains the typical cost (a per transaction cost in $) as well as a Bundle score, a mea
> Have the gains in student learning attributed to education technology justified colleges’ spending in this area? As part of Inside Higher Ed’s 2016 Survey of Faculty Attitudes on Technology, academic professionals, pro
> The financial services call center in Problem 3.66 also monitors call duration, which is the amount of time spent speaking to customers on the phone. The file CallDuration contains the following data for time, in seconds, spent by agents talking to 50 cu
> The CMO Survey collects and disseminates the opinions of top marketers in order to predict the future of markets, track marketing excellence, and improve the value of marketing in firms and in society. Part of the survey is devoted to the topic of market
> Content Marketing Institute provides insights on the content marketing habits of nonprofit professionals representing a broad range of nonprofit agencies and organizations. A survey of nonprofit marketers conducted by the Content Marketing Institute indi
> To better understand the website builder market, Clutch surveyed individuals who created a website using a do-it-yourself (DIY) website builder. Respondents, categorized by the type of website they built—business or personal, were asked
> 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. a. What proportion of trucks can be expected to travel between 34 an
> Chartered Institute of Personnel and Development (CIPD) provides commentary and insight about the trends and challenges facing the HR profession in its HR Outlook Report. The report represents the results of an online survey conducted in 2016 with HR pro
> Do Millennials or Gen-Xers feel more tense or stressed out at work? A survey of employed adults conducted online by Harris Interactive on behalf of the American Psychological Association revealed the following: Source: Data extracted from â€
> A survey by Accenture indicated that 64% of millennials as compared to 28% of baby boomers prefer “hybrid” investment advice—a combination of traditional advisory services and low-cost digital tools—over either a dedicated human advisor or conventional r
> What is the difference between a permutation and a combination?
> What is the difference between Counting Rule 1 and Counting Rule 2?
> Referring to the contingency table in Problem 4.10, if a marketer is selected at random, what is the probability that a. he or she plans to increase use of LinkedIn? b. he or she is a B2C marketer? c. he or she plans to increase use of LinkedIn or is a B
> In Bayes’ theorem, how does the prior probability differ from the revised probability?
> The weight of an energy bar is approximately normally distributed with a mean of 42.05 grams with a standard deviation of 0.025 gram. a. What is the probability that an individual energy bar contains less than 42.035 grams? b. If a sample of 4 energy b
> How can you use Bayes’ theorem in light of new information?
> How does the multiplication rule differ for events that are and are not independent?
> How does conditional probability relate to the concept of independence?
> In 2015, the per capita consumption of bottled water in the United States was reported to be 36.2 gallons. Source: Data extracted from bottledwater.org/economics/bottled-water-market. Assume that the per capita consumption of bottled water in the United
> What is the difference between mutually exclusive events and collectively exhaustive events?
> How can you use the general addition rule to find the probability of occurrence of event A or B?
> Which of the following events occur with a probability of zero? For each, state why or why not. a. A company is listed on the New York Stock Exchange and NASDAQ. b. A consumer owns a smartphone and a tablet. c. A cellphone is an Apple and a Samsung. d. A
> What is the difference between a simple event and a joint event?
> How will marketers change their social media use in the near future? A survey by Social Media Examiner reported that 76% of B2B marketers (marketers that focus primarily on attracting businesses) plan to increase their use of LinkedIn, as compared to 52%
> What are the differences between a priori probability, empirical probability, and subjective probability?
> There are 15 exercise bikes in a fitness store showroom. The fitness store owner wishes to select three of them to display at a fitness expo. How many ways can a group of three be selected?
> A daily lottery is conducted in which 2 winning numbers are selected out of 100 numbers. How many different combinations of winning numbers are possible?
> A student has seven books that she would like to place in her backpack. However, there is room for only four books. Regardless of the arrangement, how many ways are there of placing four books into the backpack?
> The amount of water in a two-liter bottle is approximately normally distributed with a mean of 2.05 liters with a standard deviation of 0.025 liter. a. What is the probability that an individual bottle contains less than 2.03 liters? b. If a sample of
> Four members of a group of 10 people are to be selected to a team. How many ways are there to select these four members?
> Given a normal distribution with m = 50 and s = 4, what is the probability that a. X > 43? b. X < 42? c. Five percent of the values are less than what X value? d. Between what two X values (symmetrically distributed around the mean) are 60 percent of the
> How many different ways can a senior project manager and an associate project manager be selected for an analytics project if there are eight data scientists available?
> A gardener has six rows available in his vegetable garden to place tomatoes, eggplant, peppers, cucumbers, beans, and lettuce. Each vegetable will be allowed one and only one row. How many ways are there to position these vegetables in this garden?
> Referring to Problem 4.44 how many different orders of finish are possible for the first four positions?
> The file McDonaldsStores contains the number of McDonald’s stores located in each of the 50 U.S. states and the District of Columbia, as of December 31, 2016: Source: Data extracted from bit.ly/2qJjFpF. a. Compute the mean, variance, and standard deviati
> For each of the following, state whether the events created are mutually exclusive and whether they are collectively exhaustive. a. Undergraduate business students were asked whether they were sophomores or juniors. b. Each respondent was classified by t
> The United Auto Courts Reports blog notes that the National Insurance Crime Bureau says that Miami-Dade, Broward, and Palm Beach counties account for a substantial number of questionable insurance claims referred to investigators. Assume that the number
> Spurious correlation refers to the apparent relationship between variables that either have no true relationship or are related to other variables that have not been measured. One widely publicized stock market indicator in the United States that is an e
> One theory concerning the S&P 500 Index is that if it increases during the first five trading days of the year, it is likely to increase during the entire year. From 1950 through 2016, the S&P 500 Index had these early gains in 42 years (in 2011 there wa
> 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?
> 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 do the empirical rule and the Chebyshev rule differ?
> 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
