Question: Suppose the age distribution in a city

> 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

> 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

> 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

> 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

> Give an example of how judgment sampling could be used in a study to determine how district attorneys feel about attorneys advertising on television.

> Develop a frame for the population of each of the following research projects. a) Measuring the job satisfaction of all union employees in a company. c) Interviewing passengers of a major airline about its food service. d) Studying the quality-control pr

> According to the Internal Revenue Service, income tax returns one year averaged $1,332 in refunds for taxpayers. One explanation of this figure is that taxpayers would rather have the government keep back too much money during the year than to owe it mon

> According to CBS Money Watch, the average monthly household cellular phone bill is $100. Suppose monthly household cell phone bills are normally distributed with a standard deviation of $11.35. a) What is the probability that a randomly selected monthly

> Tompkins Associates reports that the mean clear height for a Class A warehouse in the United States is 22 feet. Suppose clear heights are normally distributed and that the standard deviation is 4 feet. A Class A warehouse in the United States is randomly

> Suppose the Minitab output shown here represents the analysis of the length of home-use cell phone calls in terms of minutes. Describe the distribution of cell phone call lengths and interpret the meaning of the probability statements. Cumulative Distrib

> A manufacturing company produces a metal rod. Use the Excel output shown here to describe the weight of the rod. Interpret the probability values in terms of the manufacturing process. Normal Distribution Mean = 227 mg Standard Deviation = 2.3 mg x Value

> Shown here is a Minitab output. Suppose the data represent the number of sales associates who are working in a department store on any given retail day. Describe the distribution including the mean and standard deviation. Interpret the shape of the distr

> Incoming phone calls generally are thought to be Poisson distributed. If an operator averages 2.2 phone calls every 30 seconds, what is the expected (average) amount of time between calls? What is the probability that a minute or more would elapse betwee

> Determine the probabilities for the following normal distribution problems. a) μ = 604, σ = 56.8, x ≤ 635 b) μ = 48, σ = 12, x < 20 c) μ = 111, σ = 33.8, 100 ≤ x < 150 d) μ = 264, σ = 10.9, 250 < x < 255 e) μ = 37, σ = 4.35, x > 35 f) μ = 156, σ = 11.4, 

> 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 can

> In a recent year, the average daily circulation of the Wall Street Journal was 2,276,207. Suppose the standard deviation is 70,940. Assume the paper’s daily circulation is normally distributed. On what percentage of days would circulation pass 2,400,000?

> Supermarkets usually become busy at about 5 P.M. on weekdays because many workers stop by on the way home to shop. Suppose at that time arrivals at a supermarket’s express checkout station are Poisson distributed, with an average of .8 person/minute. If

> According to the ICAO, the average operating cost of an A320 jet airliner is $2,270 per hour. Suppose the operating costs of an A320 jet airliner are normally distributed with a standard deviation of $175 per hour. At what operating cost would only 20% o

> With the growing emphasis on technology and the changing business environment, many workers are discovering that training such as reeducation, skill development, and personal growth is of great assistance in the job marketplace. A recent Gallup survey fo

> Coastal businesses along the Gulf of Mexico from Texas to Florida worry about the threat of hurricanes during the season from June through October. Businesses become especially nervous when hurricanes enter the Gulf of Mexico. Suppose the arrival of hurr

> According to the Polk Company, a survey of households using the Internet when buying or leasing cars reported that 81% were seeking information about prices. In addition, 44% were seeking information about products offered. Suppose 75 randomly selected h

> The Federal Reserve System publishes data on family income based on its Survey of Consumer Finances. When the head of the household has a college degree, the mean before- tax family income is $85,200. Suppose that 60% of the before-tax family incomes whe

> According to figures released by the National Agricultural Statistics Service of the U.S. Department of Agriculture, the U.S. production of wheat over the past 20 years has been approximately uniformly distributed. Suppose the mean production over this p

> According to the U.S. Bureau of the Census, about 75% of commuters in the United States drive to work alone. Suppose 150 U.S. commuters are randomly sampled. a) What is the probability that fewer than 105 commuters drive to work alone? b) What is the pro

> The Conference Board published information on why companies expect to increase the number of part-time jobs and reduce full-time positions. Eighty-one percent of the companies said the reason was to get a flexible workforce. Suppose 200 companies that ex

> What is the first big change that American drivers made when gas prices significantly increased? 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

> According to the U.S. Department of Labor, the average American household spends $762 on personal care products and services per year. Suppose annual expenditures on P (410 ≤ x ≤ 825) = .636456 − .213849 = .422607personal care products and services per h

> Suppose the average speeds of passenger trains traveling from Newark, New Jersey, to Philadelphia, Pennsylvania, are normally distributed, with a mean average speed of 88 miles per hour and a standard deviation of 6.4 miles per hour. a) What is the proba

> Suppose inter arrival times at a hospital emergency room during a weekday are exponentially distributed, with an average inter arrival time of 9 minutes. If the arrivals are Poisson distributed, what would the average number of arrivals per hour be? What

> According to Bureau of Labor Statistics data, the average income for a worker in the metropolitan Boston area is $65,420. Suppose average income for a worker in the metropolitan Boston area is normally distributed with a standard deviation of $4,246. A m

> According to The Wirthlin Report, 24% of all workers say that their job is very stressful. If 60 workers are randomly selected, a) What is the probability that 17 or more say that their job is very stressful? b) What is the probability that more than 22

> The Zumper National Rent Report lists the average monthly apartment rent in various locations in the United States. According to the report, the average cost of renting a one-bedroom apartment in Houston is $1,082. Suppose that the standard deviation of