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Statistics For Business And Economics 8th Edition Paul Newbold, William Carlson, Betty Thorne - Solutions

The probability of A is 0.70, the probability of B is 0.80, and the probability of both is 0.50. What is the conditional probability of A, given B? Are A and B independent in a probability sense?
A company knows that a rival is about to bring out a competing product. It believes that this rival has three possible packaging plans (superior, normal, and cheap) in mind and that all are equally likely. Also, there are three equally likely possible marketing strategies (intense media
A financial analyst was asked to evaluate earnings prospects for seven corporations over the next year and to rank them in order of predicted earnings growth rates.a. How many different rankings are possible?b. If, in fact, a specific ordering is the result of a guess, what is the probability that
Given A = [E1, E3, E7, E9] and B = [E2, E3, E8, E9].a. What is the intersection of A intersection B?b. What is the union of A and B?c. Is the union of A and B collectively exhaustive?
A securities analyst claims that, given a specific list of 6 common stocks, it is possible to predict, in the correct order, the 3 that will perform best during the coming year. What is the probability of making the correct selection by chance?
A student committee has 6 members-4 undergraduate and 2 graduate students. A subcommittee of 3 members is to be chosen randomly so that each possible combination of 3 of the 6 students is equally likely to be selected. What is the probability that there will be no graduate students on the
The soccer league in 1 community has 5 teams. You are required to predict, in order, the top 3 teams at the end of the season. Ignoring the possibility of ties, calculate the number of different predictions you could make. What is the probability of making the correct prediction by chance?
You are 1 of 7 female candidates auditioning for 2 parts-the heroine and her best friend-in a play. Before the auditions you know nothing of the other candidates, and you assume all candidates have equal chances for the parts.a. How many distinct choices are possible for casting the two parts?b. In
A work crew for a building project is to be made up of 2 craftsmen and 4 laborers selected from a total of 5 craftsmen and 6 laborers.a. How many different combinations are possible?b. The brother of one of the craftsmen is a laborer. If the crew is selected at random, what is the probability that
A mutual fund company has 6 funds that invest in the U.S. market and 4 that invest in international markets.A customer wants to invest in two U.S. funds and 2 international funds.a. How many different sets of funds from this company could the investor choose?b. Unknown to this investor, one of the
It was estimated that 30% of all seniors on a campus were seriously concerned about employment prospects, 25% were seriously concerned about grades, and 20% were seriously concerned about both. What is the probability that a randomly chosen senior from this campus is seriously concerned about at
A video movie store owner finds that 30% of the customers entering the store ask an assistant for help and that 20% of the customers make a purchase before leaving. It is also found that 15% of all customers both ask for assistance and make a purchase. What is the probability that a customer does
A local public-action group solicits donations by telephone. For a particular list of prospects it was estimated that for any individual the probability was 0.05 of an immediate donation by credit card, 0.25 of no immediate donation but a request for further information through the mail, and 0.7 of
Given A = [E3, E5, E6, E10] and B = [E3, E4, E6, E9]a. What is the intersection of A and B?b. What is the union of A and B?c. Is the union of A and B collectively exhaustive?
A mail-order firm considers three possible events in filling an order:A: The wrong item is sent.B: The item is lost in transit.C: The item is damaged in transit.Assume that A is independent of both B and C and that B and C are mutually exclusive. The individual event probabilities are P(A) = 0.02,
A coach recruits for a college team a star player who is currently a high school senior. In order to play next year, the senior must both complete high school with adequate grades and pass a standardized test. The coach estimates that the probability the athlete will fail to obtain adequate high
Market research in a particular city indicated that during a week, 18% of all adults watch a television program oriented to business and financial issues, 12% read a publication oriented to these issues, and 10% do both.a. What is the probability that an adult in this city who watches a television
An inspector examines items coming from an assembly line. A review of his record reveals that he accepts only 8% of all defective items. It was also found that 1% of all items from the assembly line are both defective and accepted by the inspector. What is the probability that a randomly chosen
An analyst is presented with lists of 4 stocks and 5 bonds. He is asked to predict, in order, the 2 stocks that will yield the highest return over the next year and the 2 bonds that will have the highest return over the next year. Suppose that these predictions are made randomly and independently
A bank classifies borrowers as high risk or low risk. Only 15% of its loans are made to those in the high-risk category. Of all its loans, 5% are in default, and 40% of those in default were made to high-risk borrowers. What is the probability that a high-risk borrower will default?
A conference began at noon with two parallel sessions.The session on portfolio management was attended by 40% of the delegates, while the session on chartism was attended by 50%. The evening session consisted of a talk titled "Is the Random Walk Dead?" This was attended by 80% of all delegates.a.
A stock market analyst claims expertise in picking stocks that will outperform the corresponding industry norms. This analyst is presented with a list of 5 high-technology stocks and a list of 5 airline stocks, and she is invited to nominate, in order, the 3 stocks that will do best on each of
A quality-control manager found that 30% of work-related problems occurred on Mondays and that 20% occurred in the last hour of a day's shift. It was also found that 4% of worker-related problems occurred in the last hour of Monday's shift.a. What is the probability that a worker-related problem
A corporation was concerned with the basic educational skills of its workers and decided to offer a selected group of them separate classes in reading and practical mathematics. Of these workers, 40% signed up for the reading classes and 50% for the practical mathematics classes. Of those signing
A corporation takes delivery of some new machinery that must be installed and checked before it becomes available to use. The corporation is sure that it will take no more than 7 days for this installation and check to take place. Let A be the event "it will be more than 4 days before the machinery
A lawn-care service makes telephone solicitations, seeking customers for the coming season. A review of the records indicates that 15% of these solicitations produce new customers and that, of these new customers, 80% had used some rival service in the previous year. It is also estimated that, of
An editor may use all, some, or none of three possible strategies to enhance the sales of a book: a. An expensive prepublication promotion b. An expensive cover design c. A bonus for sales representatives who meet predetermined sales levels In the past, these three strategies have been applied
What is the conditional probability of €œhigh income,€ given €œnever€?
What is the conditional probability of €œlow income,€ given €œoccasional€?
What is the conditional probability of €œregular,€ given €œhigh income€?
Consider Example 3.4, with the following four basic outcomes for the Dow Jones Industrial Average over two consecutive days:O1: The Dow Jones average rises on both days.O2: The Dow Jones average rises on the first day but does not rise on the second day.O3: The Dow Jones average does not rise on
Consider two groups of students: B1, students who received high scores on tests, and B2, students who received low scores on tests. In group B1, 80% study more than 25 hours per week, and in group B2, 40% study more than 25 hours per week. What is the over involvement ratio for high study levels in
Consider two groups of students: B1, students who received high scores on tests, and B2, students who received low scores on tests. In group B1, 40% study more than 25 hours per week, and in group B2, 20% study more than 25 hours per week. What is the over involvement ratio for high study levels in
Consider two groups of students: B1, students who received high scores on tests, and B2, students who received low scores on tests. In group B1, 20% study more than 25 hours per week, and in group B2, 40% study more than 25 hours per week. What is the overinvolvement ratio for high study levels in
A survey carried out for a supermarket classified customers according to whether their visits to the store are frequent or infrequent and whether they often, sometimes, or never purchase generic products. The accompanying table gives the proportions of people surveyed in each of the six joint
A consulting organization predicts whether corporations' earnings for the coming year will be unusually low, unusually high, or normal. Before deciding whether to continue purchasing these forecasts, a stockbroker compares past predictions with actual outcomes. The accompanying table shows
Subscribers to a local newspaper were asked whether they regularly, occasionally, or never read the business section and also whether they had traded common stocks (or shares in a mutual fund) over the last year. The table shown here indicates the proportions of subscribers in six joint
A corporation regularly takes deliveries of a particular sensitive part from three subcontractors. It found that the proportion of parts that are good or defective from the total received were as shown in the following table:a. If a part is chosen randomly from all those received, what is the
Students in a business statistics class were asked what grade they expected in the course and whether they worked on additional problems beyond those assigned by the instructor. The following table gives proportions of students in each of eight joint classifications.a. Find the probability that a
The accompanying table shows proportions of computer salespeople classified according to marital status and whether they left their jobs or stayed over a period of 1 year.a. What is the probability that a randomly chosen salesperson was married? b. What is the probability that a randomly chosen
Florin Frenti operates a small, used car lot that has three Mercedes (M1, M2, M3) and two Toyotas (T1, T2). Two customers, Cezara and Anda, come to his lot, and each selects a car. The customers do not know each other, and there is no communication between them. Let the events A and B be defined as
The accompanying table shows proportions of adults in metropolitan areas, categorized as to whether they are public-radio contributors and whether or not they voted in the last election.a. What is the probability that a randomly chosen adult from this population voted?b. What is the probability
A campus student club distributed material about membership to new students attending an orientation meeting. Of those receiving this material 40% were men and 60% were women. Subsequently, it was found that 7% of the men and 9% of the women who received this material joined the club. a. Find the
An analyst attempting to predict a corporation's earnings next year believes that the corporation's business is quite sensitive to the level of interest rates. He believes that, if average rates in the next year are more than 1% higher than this year, the probability of significant earnings growth
Forty-two percent of a corporation's blue-collar employees were in favor of a modified health care plan, and 22% of its blue-collar employees favored a proposal to change the work schedule. Thirty-four percent of those favoring the health care plan modification favored the work schedule change. a.
The grades of a freshman college class, obtained after the first year of college, were analyzed. Seventy percent of the students in the top quarter of the college class had graduated in the upper 10% of their high school class, as had 50% of the students in the middle half of the college class and
Before books aimed at preschool children are marketed, reactions are obtained from a panel of preschool children. These reactions are categorized as favorable, neutral, or unfavorable. Subsequently, book sales are categorized as high, moderate, or low, according to the norms of this market. Similar
A manufacturer produces boxes of candy, each containing 10 pieces. Two machines are used for this purpose. After a large batch has been produced, it is discovered that one of the machines, which produces 40% of the total output, has a fault that has led to the introduction of an impurity into 10%
A student feels that 70% of her college courses have been enjoyable and the remainder have been boring. This student has access to student evaluations of professors and finds out that professors who had previously received strong positive evaluations from their students have taught 60% of his
Given P(A1) = 0.40, P(B1|A1) = 0.60, and P(B1|(A2) = 0.70, what is the probability of P(A1|B1)?
Given P(A1) = 0.80, P(B1|A1) = 0.60, and P(B1|A2) = 0.20, what is the probability of P(A1|B1)?
The sample space contains 5 As and 7 Bs. What is the probability that a randomly selected set of 2 will include 1 A and 1 B?
Given P(A1) = 0.50, P(B1|A1) = 0.40, and P(B1|A2) = 0.70, what is the probability of P(A1|B2)?
Given P(A1) = 0.40, P(B1|A1) = 0.60, and P(B1|A2) = 0.70, what is the probability of P(A2|B2) ?
Given P(A1) = 0.60, P(B1|A1) = 0.60, and P(B1|A2) = 0.40, what is the probability of P(B1|A1)?
A publisher sends advertising materials for an accounting text to 80% of all professors teaching the appropriate accounting course. Thirty percent of the professors who received this material adopted the book, as did 10% of the professors who did not receive the material. What is the probability
A stock market analyst examined the prospects of the shares of a large number of corporations. When the performance of these stocks was investigated one year later, it turned out that 25% performed much better than the market average, 25%, much worse, and the remaining 50%, about the same as the
You are the meat products manager for Gigantic Foods, a large retail supermarket food distributor who is studying the characteristics of its whole chicken product mix. Chickens are purchased from both Free Range Farms and Big Foods Ltd. Free Range Farms produces chickens that are fed with natural
You are evaluating the player selection process used by a major league baseball team. The team gives a bonus to 10% of the players that it signs to a contract, 30% of the players who were obtained through a trade, and the remainder did not receive a bonus. Examination of the player records for the
Suppose that you have an intelligent friend who has not studied probability. How would you explain to your friend the distinction between mutually exclusive events and independent events? Illustrate your answer with suitable examples.
State, with evidence, whether each of the following statements is true or false:a. The complement of the union of two events is the intersection of their complements.b. The sum of the probabilities of collectively exhaustive events must equal 1.c. The number of combinations of x objects chosen from
The sample space contains 6 As and 4 Bs. What is the probability that a randomly selected set of 3 will include 1 A and 2 Bs?
Explain carefully the meaning of conditional probability. Why is this concept important in discussing the chance of an event's occurrence?
Bayes' theorem is important because it provides a rule for moving from a prior probability to a posterior probability. Elaborate on this statement so that it would be well understood by a fellow student who has not yet studied probability.
State, with evidence, whether each of the following statements is true or false:a. The probability of the union of two events cannot be less than the probability of their intersection.b. The probability of the union of two events cannot be more than the sum of their individual probabilities.c. The
Distinguish among joint probability, marginal probability, and conditional probability. Provide some examples to make the distinctions clear.
State, with evidence, whether each of the following claims is true or false:a. The conditional probability of A, given B, must be at least as large as the probability of A.b. An event must be independent of its complement.c. The probability of A, given B, must be at least as large as the
Show that the probability of the union of events A and B can be written as follows: P(A ( B) = P(A) + P(B) [1 – P(A|B)]
An insurance company estimated that 30% of all automobile accidents were partly caused by weather conditions and that 20% of all automobile accidents involved bodily injury. Further, of those accidents that involved bodily injury, 40% were partly caused by weather conditions.a. What is the
A company places a rush order for wire of two thicknesses. Consignments of each thickness are to be sent immediately when they are available. Previous experience suggests that the probability is 0.8 that at least one of these consignments will arrive within a week. It is also estimated that, if the
Staff, Inc., a management consulting company, is surveying the personnel of Acme Ltd. It determined that 35% of the analysts have an MBA and that 40% of all analysts are over age 35. Further, of those who have an MBA, 30% are over age 35.a. What is the probability that a randomly chosen analyst
In a campus restaurant it was found that 35% of all customers order vegetarian meals and that 50% of all customers are students. Further, 25% of all customers who are students order vegetarian meals.a. What is the probability that a randomly chosen customer both is a student and orders a vegetarian
Show the probability distribution function of the face values of a single die when a fair die is rolled.
George Allen has asked you to analyze his stock portfolio, which contains 10 shares of stock D and 5 shares of stock C. The joint probability distribution of the stock prices is shown in Table 4.10. Compute the mean and variance for the total value of his stock portfolio.
Consider a country that imports steel and exports automobiles. The value per unit of cars exported is measured in units of thousands of dollars per car by the random variable X. The value per unit of steel imported is measured in units of thousands of dollars per ton of steel by the random variable
Delta International delivers approximately one million packages a day between East Asia and the United States. A random sample of the daily number of package delivery failures over the past six months provided the following results: 15, 10, 8, 16, 12, 11, 9, 8, 12, 9, 10, 8, 7, 16, 14, 12, 10, 9,
Bright Star Financial Advisers receives a mean of 19.5 applications per week for a personal financial review.Each review requires one day of an analyst's time to prepare a review. Assume that requests received during any week are assigned to an analyst for completion during the following week. If
Federated South Insurance Company has developed a new screening program for selecting new sales agents. Their past experience indicates that 20% of the new agents hired fail to produce the minimum sales in their first year and are dismissed. Their expectation is that this new screening program will
Yoshida Toimi is a candidate for the mayor of a medium-sized Midwestern city. If he receives more than 50% of the votes, he will win the election. Prior to the election, his campaign staff is planning to ask 100 randomly selected voters if they support Yoshida. a. How many positive responses from
Faschip, Ltd., is a new African manufacturer of notebook computers. Their quality target is that 99.999% of the computers they produce will perform exactly as promised in the descriptive literature. In order to monitor their quality performance they include with each computer a large piece of paper
Show the probability distribution function of the number of heads when three fair coins are tossed independently.
Let the random variable represent the number of times that you will miss class this semester. Prepare a table that shows the probability distribution and the cumulative probability distribution.
The number of computers sold per day at Dan€™s Computer Works is defined by the following probability distribution:a. P(3 ‰¤ x b. P(x > 3) =? c. P(x ‰¤ 4) =? d. P(2
American Travel Air has asked you to study flight delays during the week before Christmas at Midway Airport. The random variable X is the number of flights delayed per hour.a. What is the cumulative probability distribution?b. What is the probability of five or more delayed flights?c. What is the
Consider the probability distribution function.a. Graph the probability distribution function.b. Calculate and graph the cumulative probability distribution.c. Find the mean of the random variable X.d. Find the variance of X.
Given the probability distribution function:a. Graph the probability distribution function.b. Calculate and graph the cumulative probability distribution.c. Find the mean of the random variable X.d. Find the variance of X.
Consider the probability distribution functiona. Graph the probability distribution function.b. Calculate and graph the cumulative probability distribution.c. Find the mean of the random variable X.d. Find the variance of X.
An automobile dealer calculates the proportion of new cars sold that have been returned a various numbers of times for the correction of defects during the warranty period. The results are shown in the following table.a. Graph the probability distribution function.b. Calculate and graph the
A company specializes in installing and servicing central-heating furnaces. In the prewinter period, service calls may result in an order for a new furnace. The following table shows estimated probabilities for the numbers of new furnace orders generated in this way in the last two weeks of
Forest Green Brown, Inc., produces bags of cypress mulch. The weight in pounds per bag varies, as indicated in the accompanying table.a. Graph the probability distribution.b. Calculate and graph the cumulative probability distribution.c. What is the probability that a randomly chosen bag will
A municipal bus company has started operations in a new subdivision. Records were kept on the numbers of riders on one bus route during the early-morning weekday service. The accompanying table shows proportions over all weekdays.a. Graph the probability distribution.b. Calculate and graph the
a. A very large shipment of parts contains 10% defectives. Two parts are chosen at random from the shipment and checked. Let the random variable X denote the number of defectives found. Find the probability distribution of this random variable.b. A shipment of 20 parts contains 2 defectives. Two
A student needs to know details of a class assignment that is due the next day and decides to call fellow class members for this information. She believes that for any particular call, the probability of obtaining the necessary information is 0.40. She decides to continue calling class members
A college basketball player who sinks 75% of her free throws comes to the line to shoot a "one and one" (if the first shot is successful, she is allowed a second shot, but no second shot is taken if the first is missed; one point is scored for each successful shot). Assume that the outcome of the
A professor teaches a large class and has scheduled an examination for 7:00 p.m. in a different classroom. She estimates the probabilities in the table for the number of students who will call her at home in the hour before the examination asking where the exam will be held.Find the mean and
Students in a large accounting class were asked to rate the course by assigning a score of 1, 2, 3, 4, or 5 to the course. A higher score indicates that the students received greater value from the course. The accompanying table shows proportions of students rating the course in each category.Find
A store owner stocks an out-of-town newspaper that is sometimes requested by a small number of customers. Each copy of this newspaper costs her 70 cents, and she sells them for 90 cents each. Any copies left over at the end of the day have no value and are destroyed.Any requests for copies that
A factory manager is considering whether to replace a temperamental machine. A review of past records indicates the following probability distribution for the number of breakdowns of this machine in a week.a. Find the mean and standard deviation of the number of weekly breakdowns.b. It is estimated
An investor is considering three strategies for a $1,000 investment. The probable returns are estimated as follows: • Strategy 1: A profit of $10,000 with probability 0.15 and a loss of $1,000 with probability 0.85 • Strategy 2: A profit of $1,000 with probability 0.50, a profit of $500 with

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