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

The editor of a textbook publishing company is trying to decide whether to publish a proposed business statistics textbook. Information on previous textbooks published indicates that 10% are huge successes, 20% are modest successes, 40% break even, and 30% are losers. However, before a publishing
A municipal bond service has three rating categories (A, B, and C). Suppose that in the past year, of the municipal bonds issued throughout the United States, 70% were rated A, 20% were rated B, and 10% were rated C. Of the municipal bonds rated A, 50% were issued by cities, 40% by suburbs, and 10%
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 probability that if you randomly select a
Consider the following contingency table:What is the probability ofa. event A'?b. event A and B?c. event A' and B'?d. event A' or B'?
a. If a coin is tossed seven times, how many different outcomes are possible?b. If a die is tossed seven times, how many different outcomes are possible?c. Discuss the differences in your answers to (a) and (b).
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 next time the competition is held. c.
What are the differences between a priori probability, empirical probability, and subjective probability? Discuss.
How does the multiplication rule differ for events that are and are not independent? Discuss.
For each of the following, state whether the events created are mutually exclusive and collectively exhaustive. a. Registered voters in the United States were asked whether they are registered as Republicans or Democrats. b. Each respondent was classified by the type of car he or she drives: sedan,
A survey by the Pew Research Center ("Snapshots: Goals of 'Gen Next' vs. 'Gen X,'" USA Today, March 27, 2007, p. 1A) indicated that 81% of 18- to 25-year-olds had getting rich as a goal, as compared to 62% of 26- to 40-yearolds. Suppose that the survey was based on 500 respondents from each of the
The owner of a restaurant serving Continental-style entrées was interested in studying ordering patterns of patrons for the Friday-to-Sunday weekend time period.Records were maintained that indicated the demand for dessert during the same time period. The owner decided to study two other
Which meal are people most likely to order at a drivethrough? A survey was conducted in 2009, but the sample sizes were not reported. Suppose the results, based on a sample of 100 males and 100 females, were as follows:If a respondent is selected at random, what is the probability that he or she a.
According to a Gallup Poll, companies with employees who are engaged with their workplace have greater innovation, productivity, and profitability, as well as less employee turnover. A survey of 1,895 workers in Germany found that 13% of the workers were engaged, 67% were not engaged, and 20% were
Sport utility vehicles (SUVs), vans, and pickups are generally considered to be more prone to roll over than cars. In 1997, 24.0% of all highway fatalities involved rollovers; 15.8% of all fatalities in 1997 involved SUVs, vans, and pickups, given that the fatality involved a rollover. Given that a
Construct contingency tables of type and fees, type and risk, and fees and risk. a. For each of these contingency tables, compute all the conditional and marginal probabilities. b. Based on (a), what conclusions can you reach about whether these variables are independent?
Problem 1.27 on page 14 describes a survey of 62 undergraduate students (see the file UndergradSurvey). For these data, construct contingency tables of gender and major, gender and graduate school intention, gender and employment status, gender and computer preference, class and graduate school
Problem 1.28 on page 15 describes a survey of 44 MBA students (stored in GradSurvey). For these data, construct contingency tables of gender and graduate major, gender and undergraduate major, gender and employment status, gender and computer preference, graduate major and undergraduate major,
Which of the following events occur with a probability of zero? For each, state why or why not. a. A voter in the United States is registered as a Republican and as a Democrat. b. A voter in the United States is female and registered as a Republican. c. An automobile is a Ford and a Toyota. d. An
Does it take more time to be removed from an email list than it used to take? A study of 100 large online retailers revealed the following:a. Give an example of a simple event. b. Give an example of a joint event. c. What is the complement of "Needs three or more clicks to be removed from an email
Referring to the contingency table in Problem 4.8, if a large online retailer is selected at random, what is the probability thata. you needed three or more clicks to be removed from an email list?b. you needed three or more clicks to be removed from an email list in 2009?c. you needed three or
Given the following probability distributions:a. Compute the expected value for each distribution.b. Compute the standard deviation for each distribution.c. Compare the results of distributions A and B.
The process of being served at a bank consists of two independent parts-the time waiting in line and the time it takes to be served by the teller. Suppose that the time waiting in line has an expected value of 4 minutes, with a standard deviation of 1.2 minutes, and the time it takes to be served
In the portfolio example in this section (see page 186), half the portfolio assets are invested in the Dow Jones fund and half in a weak-economy fund. Recalculate the portfolio expected return and the portfolio risk if a. 30% of the portfolio assets are invested in the Dow Jones fund and 70% in a
You are trying to develop a strategy for investing in two different stocks. The anticipated annual return for a $1,000 investment in each stock under four different economic conditions has the following probability distribution:Compute thea. expected return for stock X and for stock Y.b. standard
Suppose that in Problem 5.12 you wanted to create a portfolio that consists of stock X and stock Y. Compute the portfolio expected return and portfolio risk for each of the following percentages invested in stock X:a. 30%b. 50%c. 70%d. On the basis of the results of (a) through (c), which
You are trying to develop a strategy for investing in two different stocks. The anticipated annual return for a $1,000 investment in each stock under four different economic conditions has the following probability distribution:Compute thea. expected return for stock X and for stock Y.b. standard
Suppose that in Problem 5.14 you wanted to create a portfolio that consists of stock X and stock Y. Compute the portfolio expected return and portfolio risk for each of the following percentages invested in stock X:a. 30%b. 50%c. 70%d. On the basis of the results of (a) through (c), which
You plan to invest $1,000 in a corporate bond fund or in a common stock fund. The following information about the annual return (per $1,000) of each of these investments under different economic conditions is available, along with the probability that each of these economic conditions will
Suppose that in Problem 5.16 you wanted to create a portfolio that consists of the corporate bond fund and the common stock fund. Compute the portfolio expected return and portfolio risk for each of the following situations:a. $300 in the corporate bond fund and $700 in the common stock fund.b.
If n = 5 and π = 0.40, what is the probability thata. X = 4?b. X ≤ 3?c. X < 2?d. X > 1?
Determine the following:a. For n = 4 and π = 0.12, what is P(X = 0)?b. For n = 10 and π = 0.40, what is P(X = 9)?c. For n = 10 and π = 0.50, what is P(X = 8)?d. For n = 6 and π = 0.83, what is P(X = 5)?
The following table contains the probability distribution for the number of traffic accidents daily in a small city:Number of Accidents Daily (X) P(X =
Determine the mean and standard deviation of the random variable X in each of the following binomial distributions:a. n = 4 and π = 0.10b. n = 4 and π = 0.40c. n = 5 and π = 0.80d. n = 3 and π = 0.50
The U.S. Department of Transportation reported that in 2009, Southwest led all domestic airlines in on-time arrivals for domestic flights, with a rate of 0.825. Using the binomial distribution, what is the probability that in the next six flightsa. Four flights will be on time?b. All six flights
A student is taking a multiple-choice exam in which each question has four choices. Assume that the student has no knowledge of the correct answers to any of the questions. She has decided on a strategy in which she will place four balls (marked A, B, C, and D) into a box. She randomly selects one
Investment advisors agree that near-retirees, defined as people aged 55 to 65, should have balanced portfolios. Most advisors suggest that the near-retirees have no more than 50% of their investments in stocks. However, during the huge decline in the stock market in 2008, 22% of nearretirees had
When a customer places an order with Rudy's On- Line Office Supplies, a computerized accounting information system (AIS) automatically checks to see if the customer has exceeded his or her credit limit. Past records indicate that the probability of customers exceeding their credit limit is 0.05.
In Example 5.4 on page 195, you and two friends decided to go to Wendy's. Now, suppose that instead you go to Popeye's, which last month filled approximately 84.8% of orders correctly. What is the probability thata. All three orders will be filled correctly?b. None of the three will be filled
You and two friends decided to go to Wendy's. Now, suppose that instead you go to McDonald's, which last month filled approximately 90.1% of the orders correctly. What is the probability thata. all three orders will be filled correctly?b. none of the three will be filled correctly?c. at least two
Assume a Poisson distribution.a. If λ = 2.5, find P(X = 2)b. If λ = 8.0, find P(X = 8)c. If λ = 0.5, find P(X = 1)d. If λ = 3.7, find P(X = 0)
Assume a Poisson distribution.a. If λ = 2.0, find P(X ≥ 2).b. If λ = 8.0, find P(X ≥ 3).c. If λ = 0.5, find P(X ≤ 1).d. If λ = 4.0, find P(X ≥ 1).e. If λ = 5.0, find P(X ≤ 3). Discuss.
Recently, a regional automobile dealership sent out fliers to perspective customers, indicating that they had already won one of three different prizes: a Kia Optima valued at $15,000, a $500 gas card, or a $5Wal-Mart shopping card. To claim his or her prize, a prospective customer needed to
Assume a Poisson distribution with λ = 5.0. What is the probability thata. X = 1?b. X < 1?c. X > 1?d. X ≤ 1?
Assume that the number of network errors experienced in a day on a local area network (LAN) is distributed as a Poisson random variable. The mean number of network errors experienced in a day is 2.4. What is the probability that in any given daya. Zero network errors will occur?b. Exactly one
The quality control manager of Marilyn's Cookies is inspecting a batch of chocolate-chip cookies that has just been baked. If the production process is in control, the mean number of chip parts per cookie is 6.0. What is the probability that in any particular cookie being inspecteda. Fewer than
Refer to Problem 5.32. How many cookies in a batch of 100 should the manager expect to discard if company policy requires that all chocolate-chip cookies sold have at least four chocolate-chip parts?In problemThe quality control manager of Marilyn's Cookies is inspecting a batch of chocolate-chip
The U.S. Department of Transportation maintains statistics for mishandled bags per 1,000 airline passengers. In the first nine months of 2009, airlines had mishandled 3.89 bags per 1,000 passengers. What is the probability that in the next 1,000 passengers, airlines will havea. No mishandled
The U.S. Department of Transportation maintains statistics for consumer complaints per 100,000 airline passengers. In the first nine months of 2009, consumer complaints were 0.99 per 100,000 passengers. What is the probability that in the next 100,000 passengers, there will bea. No complaints?b. At
Based on past experience, it is assumed that the number of flaws per foot in rolls of grade 2 paper follows a Poisson distribution with a mean of 1 flaw per 5 feet of paper (0.2 flaw per foot). What is the probability that in aa. 1-foot roll, there will be at least 2 flaws?b. 12-foot roll, there
J.D. Power and Associates calculates and publishes various statistics concerning car quality. The initial quality score measures the number of problems per new car sold. For 2009 model cars, Ford had 1.02 problems per car and Dodge had 1.34 problems per car (data extracted from S. Carty, "U.S.
Refer to Problem 5.37. If you purchased a 2009 Dodge, what is the probability that the new car will havea. Zero problems?b. Two or fewer problems?c. Compare your answers in (a) and (b) to those for the Ford in Problem 5.37 (b) and (c).In problem 5.37J.D. Power and Associates calculates and
Refer to Problem 5.37. Another article reported that in 2008, Ford had 1.12 problems per car and Dodge had 1.41 problems per car (data extracted from S. Carty, "Ford Moves Up in Quality Survey," USA Today, June 5, 2008, p. 3B). If you purchased a 2008 Ford, what is the probability that the new car
In the carnival game Under-or-Over-Seven, a pair of fair dice is rolled once, and the resulting sum determines whether the player wins or loses his or her bet. For example, the player can bet $1 that the sum will be under 7-that is, 2, 3, 4, 5, or 6. For this bet, the player wins $1 if the result
Refer to Problem 5.39. If you purchased a 2008 Dodge, what is the probability that the new car will havea. Zero problems?b. Two or fewer problems?c. Compare your answers in (a) and (b) to those for the 2009 Dodge in Problem 5.38 (a) and (b).
A toll-free phone number is available from 9 A.M. to 9 P.M. for your customers to register complaints about a product purchased from your company. Past history indicates that an average of 0.8 calls is received per minute.1. What properties must be true about the situation described here in order
Determine the following:a. If n = 4, N = 10 and A = 5, find P(X = 3).b. If n = 4, N = 6 and A = 3, find P(X = 1).c. If n = 5, N = 12 and A = 3, find P(X = 0).d. If n = 3, N = 10 and A = 3, find P(X = 3).
Referring to Problem 5.42, compute the mean and standard deviation for the hypergeometric distributions described in (a) through (d).a. If n = 4, N = 10 and A = 5, find P(X = 3).b. If n = 4, N = 6 and A = 3, find P(X = 1).c. If n = 5, N = 12 and A = 3, find P(X = 0).d. If n = 3, N = 10 and A = 3,
An auditor for the Internal Revenue Service is selecting a sample of 6 tax returns for an audit. If 2 or more of these returns are "improper," the entire population of 100 tax returns will be audited. What is the probability that the entire population will be audited if the true number of improper
The dean of a business school wishes to form an executive committee of 5 from among the 40 tenured faculty members at the school. The selection is to be random, and at the school there are 8 tenured faculty members in accounting. What is the probability that the committee will containa. None of
From an inventory of 30 cars being shipped to a local automobile dealer, 4 are SUVs. What is the probability that if 4 cars arrive at a particular dealership,a. All 4 are SUVs?b. None are SUVs?c. At least 1 is an SUV?d. What are your answers to (a) through (c) if 6 cars being shipped are SUVs?
A state lottery is conducted in which 6 winning numbers are selected from a total of 54 numbers. What is the probability that if 6 numbers are randomly selected,a. All 6 numbers will be winning numbers?b. 5 numbers will be winning numbers?c. None of the numbers will be winning numbers?d. What are
In Example 5.6 on page 203, a financial analyst was facing the task of selecting bond mutual funds to purchase for a client's portfolio. Suppose that the number of funds had been narrowed to 12 funds instead of the ten funds (still with 6 short-term corporate funds) in Example 5.6. What is the
The number of arrivals per minute at a bank located in the central business district of a large city was recorded over a period of 200 minutes, with the following results:Arrivals
What are the four properties that must be present in order to use the binomial distribution? Discuss.
What are the four properties that must be present in order to use the Poisson distribution? Discuss.
When do you use the hypergeometric distribution instead of the binomial distribution?
Darwin Head, a 35-year-old sawmill worker, won $1 million and a Chevrolet Malibu Hybrid by scoring 15 goals within 24 seconds at the Vancouver Canucks National Hockey League game (B. Ziemer, "Darwin Evolves into an Instant Millionaire," Vancouver Sun, February 28, 2008, p. 1). Head said he would
Between 1896 when the Dow Jones Index was created and 2009, the index rose in 64% of the years (data extracted from M. Hulbert, "What the Past Can't Tell Investors," The NewYork Times, January 3, 2010, p. BU2). Based on this information, and assuming a binomial distribution, what do you think is
In late 2007, it was reported that 79% of U.S. adults owned a cell phone (data extracted from E. C. Baig, "Tips Help Navigate Tech-Buying Maze," USA Today, November 28, 2007, p. 5B). Suppose that by the end of 2009, that percentage was 85%. If a sample of 10 U.S. adults is selected, what is the
One theory concerning the Dow Jones Industrial Average is that it is likely to increase during U.S. presidential election years. From 1964 through 2008, the Dow Jones Industrial Average increased in 9 of the 12 U.S. presidential election years. Assuming that this indicator is a random event with no
Errors in a billing process often lead to customer dissatisfaction and ultimately hurt bottom-line profits. An article in Quality Progress (L. Tatikonda, "A Less Costly Billing Process," Quality Progress, January 2008, pp. 30-38) discussed a company where 40% of the bills prepared contained errors.
Refer to Problem 5.57. Suppose that a quality improvement initiative has reduced the percentage of bills containing errors to 20%. If 10 bills are processed, what is the probability that a. 0 bills will contain errors? b. Exactly 1 bill will contain an error? c. 2 or more bills will contain
A study by the Center for Financial Services Innovation showed that only 64% of U.S. income earners aged 15 and older had bank accounts (A. Carrns, "Banks Court a New Client," TheWall Street Journal, March 16, 2007, p. D1). If a random sample of 20 U.S. income earners aged 15 and older is selected,
The manager of the commercial mortgage department of a large bank has collected data during the past two years concerning the number of commercial mortgages approved per week. The results from these two years (104 weeks) indicated the following:Number of CommercialMortgages Approved
One of the biggest frustrations for the consumer electronics industry is that customers are accustomed to returning goods for any reason (C. Lawton, "The War on Returns," The Wall Street Journal, May 8, 2008, pp. D1, D6). Recently, it was reported that returns for "no trouble found" were 68% of all
Refer to Problem 5.60. In the same time period, 27% of the returns were for "buyer's remorse."a. What is the expected value, or mean, of the binomial distribution?b. What is the standard deviation of the binomial distribution?c. What is the probability that none of the 20 customers made a return
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 2009, the S&P 500 Index had these early gains in 38 years. In 33 of these 38 years, the S&P 500 Index
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 example of spurious correlation is the
Approximately 300 million golf balls were lost in the United States in 2009. Assume that the number of golf balls lost in an 18-hole round is distributed as a Poisson random variable with a mean of 5 balls.a. What assumptions need to be made so that the number of golf balls lost in an 18-hole round
According to a Virginia Tech survey, college students make an average of 11 cell phone calls per day. Moreover, 80% of the students surveyed indicated that their parents pay their cell phone expenses (J. Elliot, "Professor Researches Cell Phone Usage Among Students," www. physorg.com, February 26,
Mega Millions is one of the most popular lottery games in the United States. Virtually all states participate in Mega Millions. Rules for playing and the list of prizes in most states are given below (see megamillions.com).Rules:• Select five numbers from a pool of numbers from 1 to 52 and one
Given the following probability distributions for variables X and Y:Computea. E(X) and E(Y).b. Ïƒx and Ïƒy.c. Ïƒxy.d. E(X + Y).
Given the following probability distributions for variables X and Y:Computea. E(X) and E(Y).b. Ïƒx and Ïƒy.c. Ïƒxy.d. E(X + Y).
Two investments, X and Y, have the following characteristics:If the weight of portfolio assets assigned to investment X is 0.4, compute the a. portfolio expected return. b. portfolio risk.
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 1.57?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 than 1.84?
A set of final examination grades in an introductory statistics course is normally distributed, with a mean of 73 and a standard deviation of 8.a. What is the probability that a student scored below 91 on this exam?b. What is the probability that a student scored between 65 and 89?c. The
A statistical analysis of 1,000 long-distance telephone calls made from the headquarters of the Bricks and Clicks Computer Corporation indicates that the length of these calls is normally distributed, with μ = 240 seconds and σ = 40 seconds.a. What is the probability that a call lasted less than
In 2008, the per capita consumption of coffee in Sweden was reported to be 8.2 kg, or 18.04 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 Sweden is approximately distributed as a normal
Many manufacturing problems involve the matching of machine parts, such as shafts that fit into a valve hole. A particular design requires a shaft with a diameter of 22.000 mm, but shafts with diameters between 21.990 mm and 22.010 mm are acceptable. Suppose that the manufacturing process yields
Show that for a sample of n = 39, the smallest and largest Z values are - 1.96 and + 1.96, and the middle (i.e., 20th) Z value is 0.00.
The file SUV contains the overall miles per gallon (MPG) 2010 of small SUVs (n - 26):Decide whether the data appear to be approximately normally distributed bya. Comparing data characteristics to theoretical properties.b. Constructing a normal probability plot.
As player salaries have increased, the cost of attending baseball games has increased dramatically. The file BBCost contains the cost of four tickets, two beers, four soft drinks, four hot dogs, two game programs, two baseball caps, and the parking fee for one car for each of the 30 Major League
The file Property Taxes contains the property taxes per capita for the 50 states and the District of Columbia. Decide whether the data appear to be approximately normally distributed bya. Comparing data characteristics to theoretical properties.b. Constructing a normal probability plot.
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. On March 29, 2010, the market capitalization
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 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% of all possible Z values are larger?d. Between
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 the automobile company. The data come from a
The file SavingsRatio-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.For each type of investment, decide whether the data appear to be approximately normally distributed bya. Comparing data
The file Utility contains the electricity costs, in dollars, during July 2010 for a random sample of 50 one-bedroom apartments in a large city:Decide whether the data appear to be approximately normally distributed by a. Comparing data characteristics to theoretical properties. b. Constructing a
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 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 be1. Less than 20 seconds?2. Between 10 and 30 seconds?3. More than 35 seconds?4.

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