1. According to the National Association of Insurance Commissioners (NAIC), the average premium for homeowner’s insurance in the United States in a recent year was $1,034. Suppose these premium rates are uniformly distributed across the country from $535 to $1,533. What percentage rates are between $800 and $1,200? What percentage are more than $1,350? 2. A study by Quadrant Information Services commissioned by Insure.com calculated auto insurance rates for each of the 50 states; and as a result, the average annual rate for the United States was $1,317. Suppose annual rates of auto insurance in the United States are normally distributed with a standard deviation of $324. Based on these data, what is the probability that a randomly selected auto insurance rate in the United States would be greater than $1,750? What percentage of auto insurance rates would be less than $1,200? What percentage of auto insurance rates would be between $1,100 and $1,500? 3. Homeowners do not make insurance claims very often. In fact, the Oregon Insurance Division says that, on average, a homeowner makes one claim every 9 years. Suppose such homeowner claims are Poisson distributed. What is the probability that it would be 15 years or more between claims for a homeowner? What percentage of the time would it be less than 5 years between claims? According to data released by the Insurance Information Institute, the claim frequency for automobile collisions is 5.59 per 100 car years (a car year is equal to 365 days of insured coverage for one vehicle). What is the average “inter arrival time” for auto collisions in car years? What do you think this average means? Assume that auto collisions are Poisson distributed. USAA USAA, the United Services Automobile Association, is a diversified financial services group of companies based in San Antonio, Texas. Currently, ranked 52nd in net worth and 100th in revenue in Fortune 500 companies, USAA offers banking, investing, and insurance to people and families that serve, or served, in the U.S. military. At the end of last year, there were 12.4 million members, 50.7 million products, and 32,700 employees. It is the 4th largest homeowners’ insurer and the 5th largest auto insurer. USAA was founded in 1922 by 25 army officers who came together in San Antonio and decided to insure each other’s automobiles. In the 1930s, even with the Great Depression, the number of employees doubled from 46 to 99. By 1940, there were 30,000 members including 60% of all eligible U.S. military officers. During the 1940s, in spite of a decrease in driving due to wartime restrictions on gasoline, spare parts, and tires, USAA grew rapidly and reported a profit of over $3 million. At the end of the 1950s, profits were over $14 million. In 1961, USAA’s bylaws were changed such that membership no longer had to be relinquished when an officer leaves the service. In 1963, the USAA Life Insurance Company was formed; and by the end of 1969, there were 700,000 members producing a profit of almost $24 million. In 1977, USAA reached $1 billion in assets; and in 1983 they opened the USAA Federal Savings Bank. Fortune magazine named USAA one of “America’s Most Admired Companies” in 1992 and Money magazine named USAA Federal Savings Bank the best bank in America. By the turn of the century, USAA owned and operated a total of $58.9 billion assets. By 2003, 96% of all active-duty officers and 44% of enlisted personnel were USAA members. USAA introduced a car-buying service in 2008; and in 2009, the company expanded its eligibility to all who are serving or have honorably served our nation in the U.S. military and their families. In 2011, Fortune magazine included USAA on its list of “100 Best Companies to Work For” for the third straight year. According to their mission statement, “USAA’s mission is to facilitate the financial security of its members, associates and their families by providing a full range of highly competitive financial products and services. In so doing, we seek to be the provider of choice for the military community.”
> Solve the following problems by using the binomial tables (Table A.2). Table A.2 — and cumulating the values—we have the following probability of x ≤ 2 for each value of p and the expected value (&I
> The Public Citizen’s Health Research Group studied the serious disciplinary actions that were taken during a recent year on nonfederal medical doctors in the United States. The national average was around 3.00 serious actions per 1000 doctors. A 2016 stu
> In one Midwestern city, the government has 14 repossessed houses, which are evaluated to be worth about the same amount. Ten of the houses are on the north side of town and the rest are on the west side. A local contractor submitted a bid to purchase 4 o
> The following table lists the 15 largest U.S. universities according to enrollment in a recent year. a) If five different universities are selected randomly from the list, what is the probability that exactly three of them have enrollments of more than
> According to the American Medical Association, about 36% of all U.S. physicians under the age of 35 are women. Your company has just hired eight physicians under the age of 35 and none is a woman. If a group of women physicians under the age of 35 wants
> Suppose that in the bookkeeping operation of a large corporation the probability of a recording error on any one billing is .005. Suppose the probability of a recording error from one billing to the next is constant and 1000 billings are randomly sampled
> A survey by Frank N. Magid Associates revealed that 3% of Americans are not connected to the Internet at home. Another researcher randomly selects 70 Americans. a) What is the expected number of these who would not be connected to the Internet at home? b
> One of the earliest applications of the Poisson distribution was in analyzing incoming calls to a telephone switchboard. Analysts generally believe that random phone calls are Poisson distributed. Suppose phone calls to a switchboard arrive at an average
> According to the U.S. Census Bureau, 20% of the workers in Atlanta use public transportation. If 25 Atlanta workers are randomly selected, what is the expected number to use public transportation? Graph the binomial distribution for this sample. What are
> An office in Albuquerque has 24 workers including management. Eight of the workers commute to work from the west side of the Rio Grande. Suppose 6 of the office workers are randomly selected. a) What is the probability that all 6 workers commute from the
> According to the Audit Bureau of Circulations, the top 25 city newspapers in the United States ranked according to circulation are: Rank ____________________ Newspaper 1 …………..………………………… New York Times (NY) 2 …………………………..……… Los Angeles Times (CA) 3 …………
> 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).
> A survey conducted by the Consumer Reports National Research Center reported, among other things, that women spend an average of 1.2 hours per week shopping online. Assume that hours per week shopping online are Poisson distributed. If this survey result
> A Department of Transportation survey showed that 60% of U.S. residents over 65 years of age oppose use of cell phones in flight even if there were no issues with the phones interfering with aircraft communications systems. If this information is correct
> A hair stylist has been in business one year. Sixty percent of his customers are walk-in business. If he randomly samples eight of the people from last week’s list of customers, what is the probability that three or fewer were walk-ins? If this outcome a
> According to a recent survey, the probability that a passenger files a complaint with the Department of Transportation about a particular U.S. airline is .000014. Suppose 100,000 passengers who flew with this particular airline are randomly contacted. a)
> According to Padgett Business Services, 20% of all small-business owners say the most important advice for starting a business is to prepare for long hours and hard work. Twenty-five percent say the most important advice is to have good financing ready.
> A survey conducted for the Northwestern National Life Insurance Company revealed that 70% of American workers say job stress caused frequent health problems. One in three said they expected to burn out in the job in the near future. Thirty-four percent s
> The National Center for Health Statistics reports that 25% of all Americans between the ages of 65 and 74 have a chronic heart condition. Suppose you live in a state where the environment is conducive to good health and low stress and you believe the con
> Suppose that, for every lot of 100 computer chips a company produces, an average of 1.4 are defective. Another company buys many lots of these chips at a time, from which one lot is selected randomly and tested for defects. If the tested lot contains mor
> In a particular manufacturing plant, two machines (A and B) produce a particular part. One machine (B) is newer and faster. In one five-minute period, a lot consisting of 32 parts is produced. Twenty-two are produced by machine B and the rest by machine
> A service station has a pump that distributes diesel fuel to automobiles. The station owner estimates that only about 3.2 cars use the diesel pump every 2 hours. Assume the arrivals of diesel pump users are Poisson distributed. a) What is the probabilit
> 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
> In a study by Peter D. Hart Research Associates for the Nasdaq Stock Market, it was determined that 20% of all stock investors are retired people. In addition, 40% of all U.S. adults invest in mutual funds. Suppose a random sample of 25 stock investors i
> Solve the following problems by using the hypergeometric formula. a) If N = 6, n =4, and A = 5, what is the probability that x = 3? b) If N = 10, n = 3, and A = 5, what is the probability that x ≤ 1? c) If N = 13, n = 5, and A = 3, what is the probabilit
> Use Table A.3, Appendix A, to find the following Poisson distribution values. a) P(x = 3│λ = 1.8) b) P(x < 5│λ = 3.3) c) P(x ≥ 3│λ = 2.1) d) P(2 < x ≤ 5│λ = 4.2)
> Use the Poisson formula to solve for the probabilities of the following Poisson distribution problems. a) If λ = 1.25, what is the probability that x = 4? b) If λ = 6.37, what is the probability that x ≤ 1? c) If λ = 2.4, what is the probability that x >
> Use Table A.2, Appendix A, to find the values of the following binomial distribution problems. Table A.2: a) P(x = 14│n = 20 and p = .60) b) P(x < 5│n = 10 and p = .30) c) P(x ≥ 12│n = 15 and p = .60) d) P(x > 20│n = 25 and p = .40)
> Solve for the probabilities of the following binomial distribution problems by using the binomial formula. a) If n = 11 and p = .23, what is the probability that x = 4? b) If n = 6 and p = .50, what is the probability that x ≥ 1? c) If n = 9 and p = .85,
> A western city has 18 police officers eligible for promotion. Eleven of the 18 are Hispanic. Suppose only 5 of the police officers are chosen for promotion and that 1 is Hispanic. If the officers chosen for promotion had been selected by chance alone, wh
> A company produces and ships 16 personal computers knowing that 4 of them have defective wiring. The company that purchased the computers is going to thoroughly test 3 of the computers. The purchasing company can detect the defective wiring. What is the
> Shown here are the top 10 U.S. cities ranked by population. Suppose four of these cities are randomly selected. a) What is the probability that exactly two cities are in California? b) What is the probability that none of these cities is east of the Mis
> W. Edwards Deming in his red bead experiment had a box of 4000 beads, of which 800 were red and 3200 were white. * Suppose a researcher were to conduct a modified version of the red bead experiment. In her experiment, she has a bag of 20 beads, of which
> 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 o
> The Fortune 500 includes the top 20 U.S. companies by revenue. Walmart is number one followed by Exxon Mobil and Berkshire Hathaway. Of the 20 companies on the list, 5 are in some type of healthcare-or pharmaceutical-related business. Suppose 3 firms are
> Shown here are the top 19 companies in the world in terms of oil refining capacity. Some of the companies are privately owned and others are state owned. Suppose 6 companies are randomly selected. a) What is the probability that exactly 1 company is priv
> Compute the following probabilities by using the hypergeometric formula. a) The probability of x = 3 if N = 11, A = 8, and n = 4 b) The probability of x < 2 if N = 15, A = 5, and n = 6 c) The probability of x = 0 if N = 9, A = 2, and n = 3 d) The probabi
> A data firm records a large amount of data. Historically, .9% of the pages of data recorded by the firm contain errors. If 200 pages of data are randomly selected, a) What is the probability that 6 or more pages contain errors? b) What is the probability
> A medical researcher estimates that .00004 of the population has a rare blood disorder. a) If the researcher randomly selects 100,000 people from the population, what is the probability that 7 or more people will have the rare blood disorder? b) If the r
> 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
> 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
> 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
> 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 5 minutes from 7 P.M. until 8 P.
> On Monday mornings, the First National Bank has only 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 mo
> 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 …………
> 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) λ = 6.3 b) λ = 1.3 c) λ = 8.9 d) λ = 0.6
> Find the following values by using the Poisson tables in Appendix A. a) P(x = 6│λ = 3.8) b) P(x > 7│λ = 2.9) c) P(3 ≤ x ≤ 9│λ = 4.2) d) P(x = 0│λ = 1.9) e) P(x ≤ 6│λ = 2.9) f) P(5 < x < 8│λ = 5.7
> 1. Whole Foods Market has shown steady growth at a time when traditional supermarkets have been flat. This could be attributed to a growing awareness of and demand for more natural foods. According to a study by Mintel in 2006, 30% of consumers have a hi
> 1. 3M has developed a composite measure, a 3M™ Value Index Score, which provides a standard metric to assess accountable value in healthcare. This index score is a composite measure based on six critical primary care domains derived from 16 measures of k
> For each of the following research projects, list at least one area or cluster that could be used in obtaining the sample. a) A study of road conditions in the state of Missouri. b) A study of U.S. offshore oil wells c) A study of the environmental effec
> If a company employs 3500 people and if a random sample of 175 of these employees has been taken by systematic sampling, what is the value of k? The researcher would start the sample selection between what two values? Where could the researcher obtain a
> If every 11th item is systematically sampled to produce a sample size of 75 items, approximately how large is the population?
> A city’s telephone book lists 100,000 people. If the telephone book is the frame for a study, how large would the sample size be if systematic sampling were done on every 200th person?
> According to Runzheimer International, a typical business traveler spends an average of $281 per day in Chicago. This cost includes hotel, meals, car rental, and incidentals. A survey of 65 randomly selected business travelers who have been to Chicago on
> Give a variable that could be used to stratify the population for each of the following studies. List at least four subcategories for each variable. a) A political party wants to conduct a poll prior to an election for the office of U.S. senator in Minne
> Find the following values by using the Poisson formula. a) P(x = 5│λ = 2.3) b) P(x = 2│λ = 3.9) c) P(x ≤ 3│λ = 4.1) d) P(x = 0│λ = 2.7) e) P(x = 1│λ = 5.4) f) P(4 < x
> In each of the following cases, the variable represents one way that a sample can be stratified in a study. For each variable, list some strata into which the variable can be divided. a) Age of respondent (person) b) Size of company (sales volume) c) Siz
> The U.S. Bureau of Labor Statistics released hourly wage figures for various countries for workers in the manufacturing sector. The hourly wage was $30.67 for Switzerland, $20.20 for Japan, and $23.82 for the United States. Assume that in all three count
> In a particular area of the Northeast, an estimated 75% of the homes use heating oil as the principal heating fuel during the winter. A random telephone survey of 150 homes is taken in an attempt to determine whether this figure is correct. Suppose 120 o
> Suppose you work for a large firm that has 20,000 employees. The CEO calls you in and asks you to determine employee attitudes toward the company. She is willing to commit $100,000 to this project. What are the advantages of taking a sample versus conduc
> According to the U.S. Bureau of Labor Statistics, 20% of all people 16 years of age or older do volunteer work. In this age group, women volunteer slightly more than men, with 22% of women volunteering and 19% of men volunteering. What is the probability
> Direct marketing companies are turning to the Internet for new opportunities. A recent study by Gruppo, Levey, & Co. showed that 73% of all direct marketers conduct transactions on the Internet. Suppose a random sample of 300 direct marketing companies i
> The Aluminum Association reports that the average American uses 56.8 pounds of aluminum in a year. A random sample of 51 households is monitored for one year to determine aluminum usage. If the population standard deviation of annual usage is 12.3 pounds
> The average cost of a one-bedroom apartment in a town is $850 per month. What is the probability of randomly selecting a sample of 50 one-bedroom apartments in this town and getting a sample mean of less than $830 if the population standard deviation is
> In an effort to cut costs and improve profits, many U.S. companies have been turning to outsourcing. In fact, according to Purchasing magazine, 54% of companies surveyed outsourced some part of their manufacturing process in the past two to three years.
> A directory of personal computer retail outlets in the United States contains 12,080 alphabetized entries. Explain how systematic sampling could be used to select a sample of 300 outlets.
> 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 CP
> For each of the following research projects, list three variables for stratification of the sample. a) A nationwide study of motels and hotels is being conducted. An attempt will be made to determine the extent of the availability of online links for cus
> A business analyst is conducting a study of a Fortune 500 company that has factories, distribution centers, and retail outlets across the country. How can she use cluster or area sampling to take a random sample of employees of this firm?
> Suppose you are sending out questionnaires to a randomly selected sample of 100 managers. The frame for this study is the membership list of the American Managers Association. The questionnaire contains demographic questions about the company and its top
> A survey of 2645 consumers by DDB Needham Worldwide of Chicago for public relations agency Porter/Novelli showed that how a company handles a crisis when at fault is one of the top influences in consumer buying decisions, with 73% claiming it is an influ
> Suppose the average client charge per hour for out-of-court work by lawyers in the state of Iowa is $125. Suppose further that a random telephone sample of 32 lawyers in Iowa is taken and that the sample average charge per hour for out-of-court work is $
> A company has 1250 employees, and you want to take a simple random sample of n = 60 employees. Explain how you would go about selecting this sample by using the table of random numbers. Are there numbers that you cannot use? Explain.
> A particular automobile costs an average of $21,755 in the Pacific Northwest. The standard deviation of prices is $650. Suppose a random sample of 40 dealerships in Washington and Oregon is taken and their managers are asked what they charge for this aut
> Determine a possible frame for conducting random sampling in each of the following studies. a) The average amount of overtime per week for production workers in a plastics company in Pennsylvania. b) The average number of employees in all Ralphs supermar
> Candidate Jones believes she will receive .55 of the total votes cast in her county. However, in an attempt to validate this figure, her pollster contacts a random sample of 600 registered voters in the county. The poll results show that 298 of the voter
> Suppose the age distribution in a city is as follows. Under ___________ 18 22% 18–25 ……………………….. 18% 26–50 ……………………….. 36% 51–65 ……………………….. 10% Over 65 …………………….. 14% An Analyst is conducting proportionate stratified random sampling with a sample size
> 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
> Forty-six percent of a population possesses a particular characteristic. Random samples are taken from this population. Determine the probability of each of the following occurrences. a) The sample size is 60 and the sample proportion is between .41 and
> The mean of a population is 76 and the standard deviation is 14. The shape of the population is unknown. Determine the probability of each of the following occurring from this population. a) A random sample of size 35 yielding a sample mean of 79 or more
> A Travel Weekly International Air Transport Association survey asked business travelers about the purpose for their most recent business trip. Nineteen percent responded that it was for an internal company visit. Suppose 950 business travelers are random
> According to a survey by Accountemps, 48% of executives believe that employees are most productive on Tuesdays. Suppose 200 executives are randomly surveyed. a) What is the probability that fewer than 90 of the executives believe employees are most produ
> According to a study by Decision Analyst, 21% of the people who have credit cards are very close to the total limit on the card(s). Suppose a random sample of 600 credit card users is taken. What is the probability that more than 150 credit card users ar
> If a population proportion is .28 and if the sample size is 140, 30% of the time the sample proportion will be less than what value if you are taking random samples?
> Suppose a population proportion is .40, and 80% of the time when you draw a random sample from this population you get a sample proportion of .35 or more. How large a sample were you taking?
> A population proportion is .58. Suppose a random sample of 660 items is sampled randomly from this population. a) What is the probability that the sample proportion is greater than .60? b) What is the probability that the sample proportion is between .55
> A given population proportion is .25. For the given value of n, what is the probability of getting each of the following sample proportions? a) n = 110 and ˆp ≤ .21 b) n = 33 and ˆp > .24 c) n = 59 and .24 ≤ ˆp < .27 d) n = 80 and ˆp < .30 e) n = 800 and
> According to Nielsen Media Research, the average number of hours of TV viewing by adults (18 and over) per week in the United States is 33 hours. Suppose the standard deviation is 7.9 hours and a random sample of 42 adults is taken. a) What is the probab
> 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, a87% of workers with 401(k)
> Suppose a subdivision on the southwest side of Denver, Colorado, contains 1500 houses. The subdivision was built in 1983. A sample of 100 houses is selected randomly and evaluated by an appraiser. If the mean appraised value of a house in this subdivisio
> Suppose the average checkout tab at a large supermarket is $65.12, with a standard deviation of $21.45. Twenty-three percent of the time when a random sample of 45 customer tabs is examined, the sample average should exceed what value?
> The Statistical Abstract of the United States published by the U.S. Census Bureau reports that the average annual consumption of fresh fruit per person is 99.9 pounds. The standard deviation of fresh fruit consumption is about 30 pounds. Suppose an analy
> Find the probability in each case. a) N = 1000, n = 60, μ = 60, and σ = 6; P(x̅< 76.5) =? b) N = 90, n = 36, μ = 108, and σ = 3.46; P(107 < x̅ < 107.7) =? c) N = 250, n = 100, μ = 35.6, and σ = 4.89; P(x̅ ≥ 36) =? d) N = 5000, n = 60, μ = 125, and σ = 13
> A random sample of size 81 is drawn from a population with a standard deviation of 12. If only 18% of the time a sample mean greater than 300 is obtained, what is the mean of the population?
> Suppose a random sample of size 36 is drawn from a population with a mean of 278. If 86% of the time the sample mean is less than 280, what is the population standard deviation?
> A population is normally distributed, with a mean of 23.45 and a standard deviation of 3.8. What is the probability of each of the following? a) Taking a sample of size 10 and obtaining a sample mean of 22 or more b) Taking a sample of size 4 and getting
> A population has a mean of 50 and a standard deviation of 10. If a random sample of 64 is taken, what is the probability that the sample mean is each of the following? a) Greater than 52 b) Less than 51 c) Less than 47 d) Between 48.5 and 52.4 e) Between
> Give an example of how quota sampling could be used to conduct sampling by a company test marketing a new personal computer.
> Give an example of how convenience sampling could be used in a study of Fortune 500 executives to measure corporate attitude toward paternity leave for employees.
> 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 i
