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Statistics For Business And Economics 4th Edition Paul Newbold - Solutions
Forty-two percent of blue-collar employees in a corporation were in favor of a modified health care plan, and 22% of the corporation's blue-collar employees favored a proposal to change the work schedule. Thirty-four percent of those favoring the health plan modifica tion favored the work schedule
The accompanying table shows proportions of adults in nonmetropolitan areas, catego- rized as to whether they were readers or nonreaders of newspapers and whether or not they voted in the last election." VOTED Yes No READERS NONREADERS .63 .13 .14 10 (a) What is the probability that a randomly
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 one year." MARITAL STATUS STAYED LEFT Married 64 13 Single 17 .06 (a) What is the probability that a randomly chosen salesperson was
In a survey of students in a business statistics class, students were asked what grade they expected in the course, and also whether they worked additional problems beyond those assigned by the instructor. The table gives proportions of students in each of eight joint classifications.(a) Find the
A corporation regularly takes deliveries of a particular sensitive part from three subcon- tractors. It found that the proportion of parts that are good or defective from the total re- ceived were as shown in the following table.(a) If a part is chosen randomly from all those received, what is the
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 given here shows proportions of sub- scribers in 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
A survey carried out for a supermarket classified customers according to whether their vis- its to the store are frequent or infrequent and to whether they often, sometimes, or never purchase generic products. The accompanying table gives the proportions of people sur- veyed in each of the six
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
A lawn care service makes telephone solicitations, seeking customers for the coming sea- son. A review of the records indicated that 15% of these solicitations produced new customers, and that, of these new customers, 80% had used some rival service in the pre- vious year. It was also estimated
A corporation was concerned about the basic educational skills of its workers and decided to offer a selected group of them separate classes in reading and practical mathematics. Forty percent of these workers signed up for the reading classes, and 50% for the practical mathematics classes. Of
A quality control manager found that 30% of worker-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
A stock market analyst claims expertise in picking stocks that will outperform the corre- sponding industry norms. This analyst is presented with a list of five high-technology stocks and a list of five airline stocks, and she is invited to nominate, in order, the three stocks that will do best on
A conference began at noon with two parallel sessions. The session on portfolio manage- ment 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 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 de- fault are to high-risk borrowers. What is the probability that a high-risk borrower will default?
An analyst is presented with lists of four stocks and five bonds. He is asked to predict, in order, the two stocks that will yield the highest return over the next year and the two bonds that will have the highest return over the next year. Suppose that these predictions are made randomly and
An inspector examines items coming from an assembly line. A review of her record re- veals that she 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 prob- ability that a randomly
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 ori- ented to these issues, and 10% do both. (a) What is the probability that an adult in this city, who watches a
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
A mail-order firm considers three possible foul-ups 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 event A is independent of both B and C and that events B and C are mutually exclusive. The individual event
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 .05 of an immediate donation by credit card, 25 of no immediate donation but a request for further information through the mail, and 7 of no
Refer to the information in Exercise 19, and consider the two events "Customer asks for assistance" and "Customer makes purchase." In answering the following questions, pro- vide reasons expressed in terms of probabilities of relevant events. (a) Are the two events mutually exclusive? (b) Are the
A music store owner finds that 30% of customers entering the store ask an assistant for help and that 20% make a purchase before leaving. It was also found that 15% of all cus- tomers both ask for assistance and make a purchase. What is the probability that a cus- tomer does at least one of these
It was estimated that 30% of all seniors on a campus were seriously concerned about em- ployment 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 concemed about at
A mutual fund company has six funds that invest in the U.S. market, and four that invest in foreign markets. A customer wants to invest in two U.S. funds and two foreign funds. (a) How many different sets of funds from this company could the investor choose? (b) Unknown to this investor, one of the
A work crew for a building project is to be made up of two craftsmen and four laborers se- lected from a total of five craftsmen and six laborers available. (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,
You are one of seven female candidates auditioning for two parts-the heroine and her best friend in a play. Before the auditions, you know nothing of the other candidates, and assume all candidates have equal chances for either part. (a) How many distinct choices are possible for casting the two
The senior management of a corporation has decided that in the future, it wishes to divide its advertising budget between two agencies. Eight agencies are currently being consid- ered for this work. How many different choices of two agencies are possible?
A manager has four assistants-John, George, Mary, and Jean-to assign to four tasks. Each assistant will be assigned to one of the tasks, one assistant to each task. (a) How many different arrangements of assignments are possible? (b) If assignments are made at random, what is the probability that
Baseball's American League East has five teams. You are required to predict, in order, the top three teams at the end of the season. Ignoring the possibility of ties, calculate the num- ber of different predictions you could make. What is the probability of making the correct prediction by chance?
A student committee has six members-four undergraduates and two graduate students. A subcommittee of three members is to be chosen randomly, so that each possible combina- tion of three of the six students is equally likely to be selected. What is the probability that there will be no graduate
A securities analyst claims that given a specific list of six common stocks, it is possible to predict, in the correct order, the three that will perform best during the coming year. What is the probability of making the correct selection by chance?
A company has fifty sales representatives. It decides that the most successful representa- tive during the previous year will be awarded a January vacation in Hawaii, while the sec- ond most successful will win a vacation in Las Vegas. The other representatives will be re- quired to attend a
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 simply guessed, what is the probability that
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, cheap) in mind and that all are equally likely. Also, there are three equally likely possible marketing strategies (in- tense media advertising,
A corporation receives a particular part in shipments of 100.Research has indicated the probabilities shown in the accompanying table for numbers of defective parts in a shipment. NUMBER DEFECTIVE PROBABILITY I 2 3 More than 3 29 36 .22 10 .03 (a) What is the probability there will be less than
In Section 3.4, we saw that if a pair of events are mutually exclusive, the probability of their union is the sum of their individual probabilities. However, this is not the case for events that are not mutually exclusive. Verify this assertion by considering the events A and B of Exercise 1.5. A
A manager has available a pool of eight employees who could be assigned to a project- monitoring task. Four of the employees are women and four are men. Two of the men are brothers. The manager is to make the assignment at random, so that each of the eight em- ployees is equally likely to be
A fund manager is considering investment in the stock of a health care provider. The man- ager's assessment of probabilities for rates of return on this stock over the next year are summarized in the accompanying table. Let A be the event "Rate of return will be more than 10% and B the event "Rate
A corporation takes delivery of some new machinery that must be installed and checked before it becomes operational. The accompanying table shows a manager's probability as sessment for the number of days required before the machinery becomes operational. NUMBER OF DAYS PROBABILITY 3 4 5 6 7 .08
The accompanying table shows annual percentage changes in philanthropic giving in the United States over a period of twelve years. Draw a time plot of these data and verbally in- terpret the resulting picture.
In the United States, 63% of all physicians are specialists, as are 48% in Canada, 47% in Belgium, 46% in Germany, and 37% in the United Kingdom. Draw a bar chart illustrating this information.
In 1992, revenues, in billions of dollars, for the largest media companies in three countries were 13.07 for Time Warner (U.S.), 8.41 for Bertelsmann (Germany), and 7.16 for Sony (Japan). Draw a bar chart illustrating this information.
The accompanying table shows the most important applications cited in a survey of per- sonal computer users in small businesses. Construct a pie chart to illustrate these findings. AREA Accounting Word processing Spreadsheet applications Database management CITATIONS (%) AREA CITATIONS (%) 2632 16
Draw a box-and-whisker plot to represent the data of Exercise 66 on returns of mutual funds.
The accompanying table shows percentage returns over 5 years of fifty-five corporate bond funds.(a) Represent these data with a histogram. (b) Represent these data with a stem-and-leaf diagram. (c) Draw a box-and-whisker plot for these data.
For a sample of twenty-five local companies, the accompanying table shows percentage change in output over the last three months, grouped into classes. PERCENTAGE CHANGE NUMBER OF COMPANIES For this sample: 02 2-4 46 68 8-10 3 8 7 3 (a) Draw the histogram. (b) Find and interpret the cumulative
Let X, Xxx denote the N observations in a population with mean . Let K be any number. Show that (x-K)= (x-4) + N(K - A) Hence, deduce that the value of K for which , (x-K is smallest is K-p.
A company manufactures nails, which are sold in packages. For a sample of forty pack- ages, the following numbers of nails were found in the packages. NUMBER OF NAILS 18 19 20 21 22 NUMBER OF PACKAGES 4 9 15 10 2 For this sample: (a) Find the mean number of nails per package. (b) Find the median.
The accompanying table shows the accumulated years of service before voluntary resigna- tion of 355 managerial, professional, and technical employees of a large oil company. YEARS OF SERVICE NUMBER OF EMPLOYEES YEARS OF SERVICE NUMBER OF EMPLOYEES -1 * 4 8-9 1-2 41 9-10 7 2-3 67 10-11 14 3-4 82
A sample of ten gas stations in a large city showed the following prices (in cents) for a gal- lon of regular unleaded gas for self-service customers. 96 99 104 98 103 107 103 96 99 98 (a) Find the mean. (b) Find the median. (c) Find the variance. (d) Find the standard deviation. (e) Find the
Shown below are percentage returns of the ten largest U.S. general stock mutual funds over a one-year period, ending September 17, 1993.) 27.9 12.4 11.6 22.4 17.6 26.6 15.6 18.5 22.9 25.0 For this population: (a) Find the mean. (b) Find the median. (c) Find the variance. (d) Find the standard
Draw two histograms to represent two populations with a common mean but with the stan- dard deviation of the first population larger than that of the second.
(a) Two populations each contain two members. The means of the two populations are the same, as are their standard deviations. Are the numerical values of the members of the first population necessarily the same as those of the second? (b) Two populations each contain three members. The means of
If the standard deviation of a population is zero, what can you say about the members of that population?
Explain what can be learned about a population from each of the following measures. (a) The mean (b) The median (c) The standard deviation (d) The interquartile range
Collect data on any business or economic phenomenon of interest to you. Provide a graph- ical summary that gives a clear and accurate picture of these data. Can you now produce a misleading graphical summary?
Obtain the annual report of a major U.S. corporation. Describe the graphical techniques. for data presentation used in the report and suggest any improvements that might be made.
Turn to the current day's issue of The Wall Street Journal. Discuss the procedures that are used therein for the graphical summarization of numerical information. Do the methods used present clear pictures? Can you suggest any alternative or additional graphical meth- ods that might have been used?
The accompanying table shows both higher education expenditures and public welfare ex- penditures as a percentage of total expenditures for each of the fifty states. Write an essay on these data. Use any numerical or graphical summary measures that you think are ap- propriate for the extraction of
From a local newspaper, obtain information on the advertised selling prices of homes in your area. Draw a box-and-whisker plot summarizing this information.
Refer again to the mutual funds data in Exercises 22 and 23.The two tables are arranged to coincide, so that information about any particular mutual fund is in the same location in each of the two tables. Draw a scatter plot illustrating this information and discuss its features.
Draw a box-and-whisker plot for the data of Exercise 23, which shows percentage returns for the twenty-five largest U.S. common stock mutual funds for 1989, through Thursday. November 12, 1989.
Draw a box-and-whisker plot for the data of Exercise 22, which shows percentage de- creases in share values for the twenty-five largest U.S. common stock mutual funds on Friday, November 13, 1989.
(a) Draw a box-and-whisker plot for the data of Exercise 24 on the unionization rate in the fifty states. (b) Ignoring Alaska and Hawaii, divide the country into five geographic regions. Draw on the same scale separate box-and-whisker plots for unionization in each region.
Of all alcohol advertising expenditures in the United States, 71% are on beer, 20% on dis- tilled spirits, 7% on wine, and 2% on low-alcohol beverages. Construct a pie chart to show this information.
It has been estimated that, of all U.S. business travel costs, 46% are on airfares, 23% on lodging, 11% on meals, 8% on car rentals, and 12% on other expenses. Construct a pie chart to show this information.
A recent estimate of U.S. federal budget spending showed that 46% was to entitlements, 18% to defense, 15% was grants to states and localities, 14% was interest on debt, 6% was for other federal operations, and 1% was deposit insurance. Construct a pie chart to show this information.
In 1987, there were 13,144 white and 1,190 minority graduates from U.S. medical schools. The comparable figures for 1992 were 11,525 and 1,273, respectively. Show this information on a component bar chart.
In 1986, there were 50.2 births per thousand girls aged 15-19 in the United States. For 1991, the comparable figure was 62.1. Draw a bar chart showing this information..
Over a period of thirteen years, average annual returns (in U.S. dollars) on stock markets in different countries were: Japan 18.0%, United Kingdom 17.9%, Germany 15.1%. United States 14.1%, Canada 7.7%. Draw a bar chart showing this information.
A recent estimate suggested that, in the United States, 43,000 deaths per year of women are caused by breast cancer, and 90,000 deaths per year of women are caused by diabetes. Draw a bar chart showing this information.
It was estimated that in the 1992-93 school year, 3.4 million high school boys and 1.9 mil- lion high school girls in the United States played sports. Draw a bar chart showing this information.
It has been estimated that average annual U.S. household spending is $607 on women's clothes and $345 on men's clothes. Draw a bar chart showing this information.
For households in a large town, the following information on incomes is available. HOUSEHOLD INCOME ($) 10,000-15.000 15,000-20,000 20,000-25,000 25,000-30.000 30,000-40,000 40,000-50.000 50,000-60,000 RELATIVE FREQUENCY 20 .18 .14 .12 14 14 (a) Draw the histogram. (b) Estimate the population mean
For a sample of fifty new full-size cars, fuel consumption figures were obtained and sum- marized in the accompanying table. FUEL CONSUMPTION (MILES PER GALLON) 14-16 16-18 18-20 20-22 22-24 NUMBER OF CARS 3 6 13 20 8(a) Draw the histogram. (b) Find the sample relative frequencies. (c) Find and
During a winter flu epidemic, waiting times at a student health center were longer than usual. The accompanying table summarizes the distribution of waiting times for a sample of twenty students who visited the health center in this period. WAITING TIME (HOURS) NUMBER OF STUDENTS 0-1. 1-2 2-3 3-4 6
A sample was taken of flights arriving at a major airport to study the problem of air traffic delays. The table shows numbers of minutes late for a sample of 100 flights. MINUTES LATE 0-10 10-20 20-30 30-40 40-50 50-60 NUMBER OF FLIGHTS 29 23 17 14 6 (a) Draw the histogram. (b) Find the sample
A sample of twenty financial analysts was asked to provide forecasts of earnings per share of a corporation for next year. The results are summarized in the following table. FORECAST ($ per share) 9.95-10.45 10.45-10.95 10.95-11.45 11.45-11.95 11.95-12.45 NUMBER OF ANALYSTS 2 6 3 (a) Draw the
An educational psychologist presented a task to a sample of twenty-five young children. The table shows the times spent on the task, before completing or abandoning it, by these children. TIME (MINUTES) NUMBER OF CHILDREN (a) Draw the histogram. 0-5 5-10 10-15 15-20 20-25 4 7 8 4 2 (b) Find the
For a random sample of twenty-five students from a large class, the accompanying table shows the amounts of time spent studying for a test. STUDY TIME (HOURS) NUMBER OF STUDENTS (a) Draw the histogram. 04 48 8-12 12-16 16-20 3 7 8 5 2 (b) Find the relative frequencies. (c) Find the cumulative
A corporation with new positions to fill was anxious to interview business majors on the campuses of twenty large Midwestern universities. The table shows the number of busi- ness majors from these campuses requesting interviews with the corporation. NUMBER OF STUDENTS NUMBER OF CAMPUSES (a) Draw
Refer to the data of Exercise 24 on the percentage of unionization in the fifty states. (a) Based on the data grouping used in constructing your histogram: (i) Estimate the mean of these unionization rates. (ii) Estimate the population standard deviation for these rates. (iii) Estimate the median
Refer to the data of Exercise 23 on percentage returns for the twenty-five largest U.S. common stock mutual funds. (a) Based on the data grouping used in constructing your histogram: (i) Estimate the mean for these percentage returns. (H) Estimate the population standard deviation for these
compute directly the four population summary sta- tistics estimated in part (a), and discuss the quality of these estimates.
Refer to the data of Exercise 21, which provide test scores of a class of forty students. (a) Based on the data groupings used in constructing your histogram, estimate (i) The population mean. (ii) The population standard deviation.. (iii) The median for this population. (iv) The interquartile
A sample of fifty personal property insurance policies found the following numbers of claims over the past 2 years. NUMBER OF CLAIMS NUMBER OF POLICIES 0 1 2 4 5 6 21 13 $ 4 2 3 2 (a) Find the mean number of claims per policy. (b) Find the sample median number of claims. (c) Find the modal number
The accompanying table shows percentage returns for the twenty-five largest U.S.com- mon stock mutual funds for 1989, through Thursday, November 12, 1989. (a) Construct a histogram to summarize these data. (b) Draw a stem-and-leaf diagram to summarize these data.
The accompanying table shows the percentage decreases in share values for the twenty- five largest U.S. common stock mutual funds on Friday, November 13, 1989. Construct an appropriate histogram to summarize these data.
The accompanying table shows test scores of the forty students in a class. Construct an up- propriate histogram to summarize these data. 54 56 8 59 60 62 62 67 68 70 70 73 73 75 77 79 81 81 83 85 89 89 93 93 883 86 90 90 8852885 68 73 79 83 91 94 95 98
Tires of a particular brand have lifetimes with mean 29,000 miles and standard deviation 3,000 miles. (a) Find a range in which it can be guaranteed that 75% of the lifetimes of tires of this brand lie. (b) Using the rule of thumb, find a range in which it can be estimated that approximately 95% of
In one year, earnings growth of the 500 largest U.S. corporations averaged 9.2%; the stan- dard deviation was 3.5%. (a) Find a range in which it can be guaranteed that 84% of these earnings growth figures lie. (b) Using the rule of thumb, find a range in which it can be estimated that approximately
An auditor finds that the values of a corporation's accounts receivable have mean $295 and standard deviation $63. (a) Find a range in which it can be guaranteed that 60% of these values lie. (b) Find a range in which it can be guaranteed that 80% of these values lie.
Consider the following four populations: (a) 1, 2, 3, 4, 5, 6, 7, 8 (b) 1.1, 1, 1, 8, 8, 8, 8 (c) 1.1. 4, 4, 5, 5, 8, 8 (d) -6, -3, 0, 3, 6, 9, 12, 15 All of these populations have the same mean. Without doing the calculations, arrange the populations according to the magnitudes of their variances,
A sample of twelve business statistics students found the following figures for number of hours spent studying the course material in the week before the final exam: 12 7 4 16 21 5 9311 14 10 6 (a) Find the sample mean. (b) Find the sample median. (c) Find the sample variance and standard
Refer to the data of Exercise 7 on bonus payments as a percentage of total compensation for a sample of twelve senior executives. (a) Find the sample standard deviation. (b) Find the interquartile range.
The data of Exercise 6 show percentage sales increases for ten stores. (a) Find the population variance and standard deviation.(b) Find the range. (c) Find the interquartile range.
Refer to the data of Exercise 5 on a sample of ten test scores. (a) Find the sample variance and standard deviation. (b) Find the mean absolute deviation. (c) Find the interquartile range.
The data of Exercise 4 show ratings of dormitory food service given by a sample of eight students. (a) Find the sample variance and standard deviation. (b) Find the interquartile range.
Refer to the data of Exercise 3 on a sample of ten forecasts of the percentage growth in the consumer price index. (a) Find the sample variance and standard deviation. (b) Find the interquartile range.
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