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Business Statistics Contemporary Decision Making 6th Edition Ken Black - Solutions
A pen company averages 1.2 defective pens per carton produced (200 pens). The number of defects per carton is Poisson distributed.a. What is the probability of selecting a carton and finding no defective pens?b. What is the probability of finding eight or more defective pens in a carton?c. Suppose
Ship collisions in the Houston Ship Channel are rare. Suppose the number of collisions are Poisson distributed, with a mean of 1.2 collisions every four months.a. What is the probability of having no collisions occur over a four-month period?b. What is the probability of having exactly two
The average number of annual trips per family to amusement parks in the United States is Poisson distributed, with a mean of 0.6 trips per year.What is the probability of randomly selecting an American family and finding the following?a. The family did not make a trip to an amusement park last
According to the United National Environmental Program and World Health Organization, in Mumbai, India, air pollution standards for particulate matter are exceeded an average of 5.6 days in every three-week period. Assume that the distribution of number of days exceeding the standards per
A restaurant manager is interested in taking a more statistical approach to predicting customer load. She begins the process by gathering data. One of the restaurant hosts or hostesses is assigned to count customers every five minutes from 7 P.M. until 8 P.M.every Saturday night for three weeks.
On Monday mornings, the First National Bank only has one teller window open for deposits and withdrawals. Experience has shown that the average number of arriving customers in a four-minute interval on Monday mornings is 2.8, and each teller can serve more than that number efficiently. These random
Sketch the graphs of the following Poisson distributions. Compute the mean and standard deviation for each distribution. Locate the mean on the graph. Note how the probabilities are graphed around the mean.a. l = 6.3b. l = 1.3c. l = 8.9d. l = 0.6
Find the following values by using the Poisson tables in Appendix A. a. P(x=6= 3.8) b. P(x7 = 2.9) c. P(3 x 9| = 4.2) d. P(x=0A = 1.9) 6A e. P(x 6 = 2.9) f. P(5x8|A = 5.7)
Find the following values by using the Poisson formula. a. P(x = 5A = 2.3) b. P(x 2 = 3.9) == c. P(x = 3A 4.1) d. P(x = 0 = 2.7) == e. P(x = 1 = 5.4) f. P(4x8| = 4.4)
According to Cerulli Associates of Boston, 30% of all CPA financial advisors have an average client size between $500,000 and $1 million. Thirty-four percent have an average client size between $1 million and $5 million. Suppose a complete list of all CPA financial advisors is available and 18 are
In the past few years, outsourcing overseas has become more frequently used than ever before by U.S. companies. However, outsourcing is not without problems. A recent survey by Purchasing indicates that 20% of the companies that outsource overseas use a consultant. Suppose 15 companies that
Studies have shown that about half of all workers who change jobs cash out their 401(k) plans rather than leaving the money in the account to grow. The percentage is much higher for workers with small 401(k) balances. In fact, 87% of workers with 401(k) accounts less than $5,000 opt to take their
An increasing number of consumers believe they have to look out for themselves in the marketplace. According to a survey conducted by the Yankelovich Partners for USA WEEKEND magazine, 60% of all consumers have called an 800 or 900 telephone number for information about some product. Suppose a
The Wall Street Journal reported some interesting statistics on the job market. One statistic is that 40% of all workers say they would change jobs for “slightly higher pay.” In addition, 88% of companies say that there is a shortage of qualified job candidates. Suppose 16 workers are randomly
What is the first big change that American drivers made due to higher gas prices?According to an Access America survey, 30% said that it was cutting recreational driving. However, 27% said that it was consolidating or reducing errands. If these figures are true for all American drivers, and if 20
Use the probability tables in Table A.2 and sketch the graph of each of the following binomial distributions. Note on the graph where the mean of the distribution falls.a. n = 6 and p = .70b. n = 20 and p = .50c. n = 8 and p = .80
Solve for the mean and standard deviation of the following binomial distributions.a. n = 20 and p = .70b. n = 70 and p = .35c. n = 100 and p = .50
Solve the following problems by using the binomial tables (Table A.2).a. If n = 20 and p = .50, find P(x = 12).b. If n = 20 and p = .30, find P(x 8).c. If n = 20 and p = .70, find P(x 12).d. If n = 20 and p = .90, find P(x 16).e. If n = 15 and p = .40, find P(4 x 9).f. If n = 10 and p = .60, find
Solve the following problems by using the binomial formula.a. If n = 4 and p = .10, find P(x = 3).b. If n = 7 and p = .80, find P(x = 4).c. If n = 10 and p = .60, find P(x 7).d. If n = 12 and p = .45, find P(5 x 7).
Suppose 20% of the people in a city prefer Pepsi-Cola as their soft drink of choice. If a random sample of six people is chosen, the number of Pepsi drinkers could range from zero to six. Shown here are the possible numbers of Pepsi drinkers in a sample of six people and the probability of that
The following data are the result of a historical study of the number of flaws found in a porcelain cup produced by a manufacturing firm. Use these data and the associated probabilities to compute the expected number of flaws and the standard deviation of flaws.Flaws Probability 0 .461 1 .285 2
Determine the mean, the variance, and the standard deviation of the following discrete distribution.x P(x)0 .103 1 .118 2 .246 3 .229 4 .138 5 .094 6 .071 7 .001
Determine the mean, the variance, and the standard deviation of the following discrete distribution.x P(x)1 .238 2 .290 3 .177 4 .158 5 .137
A retail study by Deloitte revealed that 54% of adults surveyed believed that plastic, noncompostable shopping bags should be banned. Suppose 41% of adults regularly recycle aluminum cans and believe that plastic, noncompostable shopping bags should be banned. In addition, suppose that 60% of
According to U.S. Census Bureau figures, 35.3% of all Americans are in the 0–24 age bracket, 14.2% are in the 25–34 age bracket, 16.0% are in the 35–44 age bracket, and 34.5 are in the 45 and older age bracket. A study by Jupiter Media Metrix determined that Americans use their leisure time
A survey by the Arthur Andersen Enterprise Group/National Small Business United attempted to determine what the leading challenges are for the growth and survival of small businesses. Although the economy and finding qualified workers were the leading challenges, several others were listed in the
A small independent physicians’ practice has three doctors.Dr. Sarabia sees 41% of the patients, Dr. Tran sees 32%, and Dr. Jackson sees the rest. Dr. Sarabia requests blood tests on 5% of her patients, Dr. Tran requests blood tests on 8% of his patients, and Dr. Jackson requests blood tests on
In a study of incentives used by companies to retain mature workers by The Conference Board, it was reported that 41% use flexible work arrangements.Suppose that of those companies that do not use flexible work arrangements, 10% give time off for volunteerism.In addition, suppose that of those
Pitney Bowes surveyed 302 directors and vice presidents of marketing at large and midsized U.S. companies to determine what they believe is the best vehicle for educating decision makers on complex issues in selling products and services. The highest percentage of companies chose direct
Companies use employee training for various reasons, including employee loyalty, certification, quality, and process improvement. In a national survey of companies, BI Learning Systems reported that 56% of the responding companies named employee retention as a top reason for training. Suppose 36%
Health Rights Hotline published the results of a survey of 2,400 people in Northern California in which consumers were asked to share their complaints about managed care. The number one complaint was denial of care, with 17% of the participating consumers selecting it.Several other complaints were
A study on ethics in the workplace by the Ethics Resource Center and Kronos, Inc., revealed that 35% of employees admit to keeping quiet when they see coworker misconduct. Suppose 75% of employees who admit to keeping quiet when they see coworker misconduct call in sick when they are well. In
The Steelcase Workplace Index studied the types of workrelated activities that Americans did while on vacation in the summer. Among other things, 40% read work-related material. Thirty-four percent checked in with the boss.Respondents to the study were allowed to select more than one activity.
A telephone survey conducted by the Maritz Marketing Research company found that 43% of Americans expect to save more money next year than they saved last year.Forty-five percent of those surveyed plan to reduce debt next year. Of those who expect to save more money next year, 81% plan to reduce
A few years ago, a survey commissioned by The World Almanac and Maturity News Service reported that 51%of the respondents did not believe the Social Security system will be secure in 20 years. Of the respondents who were age 45 or older, 70% believed the system will be secure in 20 years. Of the
In a certain city, 30% of the families have a MasterCard, 20% have an American Express card, and 25% have a Visa card. Eight percent of the families have both a MasterCard and an American Express card. Twelve percent have both a Visa card and a MasterCard. Six percent have both an American Express
According to Link Resources, 16% of the U.S. population is technology driven. However, these figures vary by region. For example, in the West the figure is 20% and in the Northeast the figure is 17%. Twenty-one percent of the U.S. population in general is in the West and 20%of the U.S. population
The U.S. Bureau of Labor Statistics publishes data on the benefits offered by small companies to their employees. Only 42% offer retirement plans while 61%offer life insurance. Suppose 33% offer both retirement plans and life insurance as benefits. If a small company is randomly selected, determine
Purchasing Survey asked purchasing professionals what sales traits impressed them most in a sales representative.Seventy-eight percent selected “thoroughness.” Forty percent responded “knowledge of your own product.” The purchasing professionals were allowed to list more than one trait.
The following probability matrix contains a breakdown on the age and gender of U.S. physicians in a recent year, as reported by the American Medical Association.a. What is the probability that one randomly selected physician is 35–44 years old?b. What is the probability that one randomly selected
Use the values in the contingency table to solve the equations given. a. P(FOA): b. P(A|B)= DEFG A 39 7 00 B 8 C 10 4 S 5. 12 6 4 3 7
Use the values in the contingency table to solve the equations given. DE A 10 20 Variable 2 B 15 5 C 30 15 a. P(E)=. b. P(BUD). c. P(ANE)= d. P(B|E)=. e. P(AUB)= f. P(BC)= g. P(D|C)=- h. P(A|B)= i. Are variables 1 and 2 independent? Why or why not?
Suppose 70% of all companies are classified as small companies and the rest as large companies. Suppose further, 82% of large companies provide training to employees, but only 18% of small companies provide training. A company is randomly selected without knowing if it is a large or small company;
In a small town, two lawn companies fertilize lawns during the summer. Tri-State Lawn Service has 72% of the market. Thirty percent of the lawns fertilized by Tri-State could be rated as very healthy one month after service. Greenchem has the other 28% of the market. Twenty percent of the lawns
Alex, Alicia, and Juan fill orders in a fast-food restaurant. Alex incorrectly fills 20%of the orders he takes. Alicia incorrectly fills 12% of the orders she takes. Juan incorrectly fills 5% of the orders he takes. Alex fills 30% of all orders, Alicia fills 45%of all orders, and Juan fills 25% of
In a manufacturing plant, machine A produces 10% of a certain product, machine B produces 40% of this product, and machine C produces 50% of this product. Five percent of machine A products are defective, 12% of machine B products are defective, and 8% of machine C products are defective. The
In a study undertaken by Catalyst, 43% of women senior executives agreed or strongly agreed that a lack of role models was a barrier to their career development.In addition, 46% agreed or strongly agreed that gender-based stereotypes were barriers to their career advancement. Suppose 77% of those
Accounting Today reported that 37% of accountants purchase their computer hardware by mail order direct and that 54% purchase their computer software by mail order direct. Suppose that 97% of the accountants who purchase their computer hardware by mail order direct purchase their computer software
According to a survey published by ComPsych Corporation, 54% of all workers read e-mail while they are talking on the phone. Suppose that 20% of those who read e-mail while they are talking on the phone write personal “to-do” lists during meetings. Assuming that these figures are true for all
Arthur Andersen Enterprise Group/National Small Business United,Washington, conducted a national survey of small-business owners to determine the challenges for growth for their businesses. The top challenge, selected by 46% of the smallbusiness owners, was the economy. A close second was finding
In a recent year, business failures in the United States numbered 83,384, according to Dun & Bradstreet. The construction industry accounted for 10,867 of these business failures. The South Atlantic states accounted for 8,010 of the business failures.Suppose that 1,258 of all business failures were
The results of a survey asking, “Do you have a calculator and/or a computer in your home?” follow.Is the variable “calculator” independent of the variable “computer”? Why or why not? Calculator Yes No Yes 46 3 49 Computer No 11 15 26 57 18 75
Use the values in the probability matrix to solve the equations given. a. P(C|A)= b. P(B|D)= c. P(A|B)=. C D A .36 .44 B .11 .09
Use the values in the contingency table to solve the equations given. a. P(G|A)=. b. P(B|F). c. P(C|E). d. P(E|G)= EFG A 15 12 8 B 11 17 19 C 21 32 27 D 18 13 12
The U.S. Energy Department states that 60% of all U.S. households have ceiling fans.In addition, 29% of all U.S. households have an outdoor grill. Suppose 13% of all U.S. households have both a ceiling fan and an outdoor grill. A U.S. household is randomly selected.a. What is the probability that
A study by Becker Associates, a San Diego travel consultant, found that 30% of the traveling public said that their flight selections are influenced by perceptions of airline safety. Thirty-nine percent of the traveling public wants to know the age of the aircraft. Suppose 87% of the traveling
According to the Consumer Electronics Manufacturers Association, 10% of all U.S.households have a fax machine and 52% have a personal computer. Suppose 91% of all U.S. households having a fax machine have a personal computer. A U.S.household is randomly selected.a. What is the probability that the
A study by Peter D. Hart Research Associates for the Nasdaq Stock Market revealed that 43% of all American adults are stockholders. In addition, the study determined that 75% of all American adult stockholders have some college education. Suppose 37% of all American adults have some college
According to the nonprofit group Zero Population Growth, 78% of the U.S. population now lives in urban areas. Scientists at Princeton University and the University of Wisconsin report that about 15% of all American adults care for ill relatives. Suppose that 11% of adults living in urban areas care
a. A batch of 50 parts contains six defects. If two parts are drawn randomly one at a time without replacement, what is the probability that both parts are defective?b. If this experiment is repeated, with replacement, what is the probability that both parts are defective?
Use the values in the probability matrix to solve the equations given. DE F A .12 .13 .08 B .18 .09 .04 C .06 .24 .06 a. P(EB)= b. P(CF)= c. P(END)=
Use the values in the contingency table to solve the equations given. a. P(AE)= = b. P(DB)=- c. P(DE) d. P(AB). CDEF A 5 11 16 8 B 2 3 5 7
A survey conducted by the Northwestern University Lindquist-Endicott Report asked 320 companies about the procedures they use in hiring. Only 54% of the responding companies review the applicant’s college transcript as part of the hiring process, and only 44% consider faculty references. Assume
According to Nielsen Media Research, approximately 67% of all U.S. households with television have cable TV. Seventy-four percent of all U.S. households with television have two or more TV sets. Suppose 55% of all U.S. households with television have cable TV and two or more TV sets. A U.S.
According to the U.S. Bureau of Labor Statistics, 75% of the women 25 through 49 years of age participate in the labor force. Suppose 78% of the women in that age group are married. Suppose also that 61% of all women 25 through 49 years of age are married and are participating in the labor force.a.
Suppose that 47% of all Americans have flown in an airplane at least once and that 28% of all Americans have ridden on a train at least once.What is the probability that a randomly selected American has either ridden on a train or flown in an airplane?Can this problem be solved? Under what
Use the values in the matrix to solve the equations given.a. P(A D) =b. P(E B) =c. P(D E) =d. P (C ´ F) =4.10 Use the values in the matrix to solve the equations given. DEF 8 12 A 5 B 10 C 00 8 99 6 4 2 5
Given P(A) = .10, P(B) = .12, P(C) = .21, P(A C) = .05, and P(B C) = .03, solve the following.a. P(A C) =b. P(B C) =c. If A and B are mutually exclusive, P(A B) =
A small company has 20 employees. Six of these employees will be selected randomly to be interviewed as part of an employee satisfaction program. How many different groups of six can be selected?
A company places a seven-digit serial number on each part that is made. Each digit of the serial number can be any number from 0 through 9. Digits can be repeated in the serial number. How many different serial numbers are possible?
A bin contains six parts. Two of the parts are defective and four are acceptable. If three of the six parts are selected from the bin, how large is the sample space? Which counting rule did you use, and why? For this sample space, what is the probability that exactly one of the three sampled parts
A company’s customer service 800 telephone system is set up so that the caller has six options. Each of these six options leads to a menu with four options. For each of these four options, three more options are available. For each of these three options, another three options are presented. If a
If a population consists of the positive even numbers through 30 and if A = {2, 6, 12, 24}, what is A ?
Given X = {1, 3, 5, 7, 8, 9}, Y = {2, 4, 7, 9}, and Z = {1, 2, 3, 4, 7}, solve the following.a.X Z = _____b. X Y= _____c. X Z = _____d. X Y Z = _____e. X Y Z = _____f. (X Y) Z = _____ g. (Y Z) (X Y) = _____ h. X or Y = _____ i. Y and X = _____
A supplier shipped a lot of six parts to a company. The lot contained three defective parts. Suppose the customer decided to randomly select two parts and test them for defects. How large a sample space is the customer potentially working with? List the sample space. Using the sample space list,
The Nielsen Company compiled a list of the top 25 advertisers in African American media. Shown below are a Minitab descriptive statistics analysis of the annual advertising spending in $ million by these companies in African American media and a box plot of these data.Study this output and
Excel was used to analyze the number of employees for the top 60 employers with headquarters around the world outside of the United States. The data was compiled by myglobalcareer.com, extracted from My Global Career 500, and was analyzed using Excel’s descriptive statistics feature. Summarize
Hispanic Business magazine publishes a list of the top 50 advertisers in the Hispanic market. The advertising spending for each of these 50 advertisers (in $ millions)was entered into a Minitab spreadsheet and the data were analyzed using Minitab’s Graphical Summary.Study the output from this
Netvalley.com compiled a list of the top 100 banks in the United States according to total assets. Leading the list was Bank of America, followed by JPMorgan Chase and Citibank. Following is an Excel analysis of total assets($ billions) of these banks using the descriptive statistics feature. Study
Runzheimer International publishes data on overseas business travel costs. They report that the average per diem total for a business traveler in Paris, France, is$349. Suppose the shape of the distribution of the per diem costs of a business traveler to Paris is unknown, but that 53% of the per
According to the U.S. Army Corps of Engineers, the top 20 U.S. ports, ranked by total tonnage (in million tons), were as follows.Port Total Tonnage South Louisiana, LA 212.7 Houston, TX 211.7 New York, NY and NJ 152.1 Huntington, WV, KY, and OH 83.9 Long Beach, CA 79.9 Beaumont, TX 78.9 Corpus
According to the Bureau of Labor Statistics, the average annual salary of a worker in Detroit, Michigan, is$35,748. Suppose the median annual salary for a worker in this group is $31,369 and the mode is $29,500. Is the distribution of salaries for this group skewed? If so, how and why? Which of
During the 1990s, businesses were expected to show a lot of interest in Central and Eastern European countries.As new markets began to open, American businesspeople needed a better understanding of the market potential there. The following are the per capita GDP figures for eight of these European
According to a Human Resources report, a worker in the industrial countries spends on average 419 minutes a day on the job. Suppose the standard deviation of time spent on the job is 27 minutes.a. If the distribution of time spent on the job is approximately bell shaped, between what two times
The Polk Company reported that the average age of a car on U.S. roads in a recent year was 7.5 years. Suppose the distribution of ages of cars on U.S. roads is approximately bellshaped. If 99.7% of the ages are between 1 year and 14 years, what is the standard deviation of car age? Suppose the
Financial analysts like to use the standard deviation as a measure of risk for a stock. The greater the deviation in a stock price over time, the more risky it is to invest in the stock. However, the average prices of some stocks are considerably higher than the average price of others, allowing
A research agency administers a demographic survey to 90 telemarketing companies to determine the size of their operations. When asked to report how many employees now work in their telemarketing operation, the companies gave responses ranging from 1 to 100.The agency’s analyst organizes the
The radio music listener market is diverse. Listener formats might include adult contemporary, album rock, top 40, oldies, rap, country and western, classical, and jazz. In targeting audiences, market researchers need to be concerned about the ages of the listeners attracted to particular formats.
The U.S. Department of the Interior releases figures on mineral production. Following are the 14 leading states in nonfuel mineral production in the United States.State Value ($ billions)Arizona 4.35 California 4.24 Nevada 3.88 Florida 2.89 Utah 2.79 Texas 2.72 Minnesota 2.19 Missouri 1.94 Georgia
Shown here are the U.S. oil refineries with the largest capacity in terms of barrels per day according to the U.S.Energy Information Administration. Use these as population data and answer the questions.Refinery Location Company Capacity Baytown, Texas ExxonMobil 567,000 Baton Rouge, Louisiana
Shown in right column are the top 10 companies receiving the largest dollar volume of contract awards from the U.S. Department of Defense in a recent year. Use this population data to compute a mean and a standard deviation for these top 10 companies.Amount of Contracts Company ($ billions)Lockheed
Shown below are the top 20 companies in the computer industry by sales according to netvalley.com in a recent year. Compute the mean, median, P30, P60, P90, Q1, Q3, range, and interquartile range on these data.Company Sales ($ millions)IBM 91,134 Hewlett Packard 86,696 Verizon Communications 75,112
The 2000 U.S. Census also asked for each person’s age.Suppose that a sample of 40 households taken from the census data showed the age of the first person recorded on the census form to be as follows.42 29 31 38 55 27 28 33 49 70 25 21 38 47 63 22 38 52 50 41 19 22 29 81 52 26 35 38 29 31 48 26
The 2000 U.S. Census asked every household to report information on each person living there. Suppose for a sample of 30 households selected, the number of persons living in each was reported as follows.2 3 1 2 6 4 2 1 5 3 2 3 1 2 2 1 3 1 2 2 4 2 1 2 8 3 2 1 1 3 Compute the mean, median, mode,
Suppose a consumer group asked 18 consumers to keep a yearly log of their shopping practices and that the following data represent the number of coupons used by each consumer over the yearly period. Use the data to construct a box-and-whisker plot. List the median, Q1, Q3, the endpoints for the
Construct a box-and-whisker plot on the following data. Do the data contain any outliers? Is the distribution of data skewed?540 690 503 558 490 609 379 601 559 495 562 580 510 623 477 574 588 497 527 570 495 590 602 541
Suppose the following data are the ages of Internet users obtained from a sample.Use these data to compute a Pearsonian coefficient of skewness.What is the meaning of the coefficient?41 15 31 25 24 23 21 22 22 18 30 20 19 19 16 23 27 38 34 24 19 20 29 17 23
The sales volumes for the top real estate brokerage firms in the United States for a recent year were analyzed using descriptive statistics. The mean annual dollar volume for these firms was $5.51 billion, the median was $3.19 billion, and the standard deviation was $9.59 billion. Compute the value
A local hotel offers ballroom dancing on Friday nights. A researcher observes the customers and estimates their ages. Discuss the skewness of the distribution of ages if the mean age is 51, the median age is 54, and the modal age is 59.
On a certain day the average closing price of a group of stocks on the New York Stock Exchange is $35 (to the nearest dollar). If the median value is $33 and the mode is $21, is the distribution of these stock prices skewed? If so, how?
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