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Business Statistics for Contemporary Decision Making 6th Edition Ken Black - Solutions
Determine the probabilities for the following normal distribution problems.a. µ = 604, σ = 56.8, x ≤ 635b. µ = 48, σ = 12, x < 20c. µ = 111, σ = 33.8, 100 ≤x < 150d. µ = 264, σ = 10.9, 250 < x < 255e. µ = 37, σ = 4.35, x > 35f. µ = 156, σ = 11.4, x ≥ 170
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 selected.a. What is the probability that the
According to a report by Scarborough Research, the average monthly household cellular phone bill is $60. Suppose local 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 cell phone bill is more
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 money at the end of the year. Suppose the
Toolworkers are subject to work-related injuries. One disorder, caused by strains to the hands and wrists, is called carpal tunnel syndrome. It strikes as many as 23,000 workers per year. The U.S. Labor Department estimates that the average cost of this disorder to employers and insurers is
Suppose you are working with a data set that is normally distributed, with a mean of 200 and a standard deviation of 47. Determine the value of x from the following information.a. 60% of the values are greater than x.b. x is less than 17% of the values.c. 22% of the values are less than x.d. x is
Suppose the annual employer 401(k) cost per participant is normally distributed with a standard deviation of $625, but the mean is unknown.a. If 73.89% of such costs are greater than $1,700, what is the mean annual employer 401(k) cost per participant?b. Suppose the mean annual employer 401(k) cost
Suppose the standard deviation for Problem is unknown but the mean is still 22 feet. If 72.4% of all U.S. Class A warehouses have a clear height greater than 18.5 feet, what is the standard deviation?
Suppose the mean clear height of all U.S. Class A warehouses is unknown but the standard deviation is known to be 4 feet.What is the value of the mean clear height if 29% of U.S. Class A warehouses have a clear height less than 20 feet?
Data accumulated by the National Climatic Data Center shows that the average wind speed in miles per hour for St. Louis,Missouri, is 9.7. Suppose wind speed measurements are normally distributed for a given geographic location. If 22.45% of the time the wind speed measurements are more than 11.6
According to Student Monitor, a New Jersey research firm, the average cumulated college student loan debt for a graduating senior is $25,760. Assume that the standard deviation of such student loan debt is $5,684. Thirty percent of these graduating seniors owe more than what amount?
Convert the following binomial distribution problems to normal distribution problems. Use the correction for continuity.a. P (x ≤ 16 | n = 30 and p = .70)b. P (10 < x ≤ 20) | n = 25 and p = .50)c. P (x = 22 | n = 40 and p = .60)d. P (x > 14 | n = 16 and p = .45)
Use the test 3 to determine whether the following binomial distributions can be approximated by using the normal distribution.a. n = 8 and p = .50b. n = 18 and p = .80c. n = 12 and p = .30d. n = 30 and p = .75e. n = 14 and p = .50
Where appropriate, work the following binomial distribution problems by using the normal curve. Also, use Table A.2 to find the answers by using the binomial distribution and compare the answers obtained by the two methods.a. P (x = 8 | n = 25 and p = .40) = ?b. P (x ≥ 13 | n = 20 and p = .60) =
The Zimmerman Agency conducted a study for Residence Inn by Marriott of business travelers who take trips of five nights or more. According to this study, 37% of these travelers enjoy sightseeing more than any other activity that they do not get to do as much at home. Suppose 120 randomly selected
One study on managers' satisfaction with management tools reveals that 59% of all managers use self-directed work teams as a management tool. Suppose 70 managers selected randomly in the United States are interviewed.What is the probability that fewer than 35 use self-directed work teams as a
According to the Yankee Group, 53% of all cable households rate cable companies as good or excellent in quality transmission. Sixty percent of all cable households rate cable companies as good or excellent in having professional personnel. Suppose 300 cable households are randomly contacted.a. What
Market researcher Gartner Dataquest reports that Dell Computer controls 27% of the PC market in the United States. Suppose a business researcher randomly selects 130 recent purchasers of PC.a. What is the probability that more than 39 PC purchasers bought a Dell computer?b. What is the probability
A study about strategies for competing in the global marketplace states that 52% of the respondents agreed that companies need to make direct investments in foreign countries. It also states that about 70% of those responding agree that it is attractive to have a joint venture to increase global
Use the probability density formula to sketch the graphs of the following exponential distributions.a. λ = 0.1b. λ = 0.3c. λ = 0.8d. λ = 3.0
Determine the mean and standard deviation of the following exponential distributions.a. λ = 3.25b. λ = 0.7c. λ = 1.1d. λ = 6.0
Determine the following exponential probabilities.a. P(x ≥ 5 | λ = 1.35)b. P(x < 3 | λ = 0.68)c. P(x > 4 | λ = 1.7)d. P(x < 6 | λ = 0.80)
The average length of time between arrivals at a turnpike tollbooth is 23 seconds. Assume that the time between arrivals at the tollbooth is exponentially distributed.a. What is the probability that a minute or more will elapse between arrivals?b. If a car has just passed through the tollbooth,
A busy restaurant determined that between 6:30 P.M. and 9:00 P.M. on Friday nights, the arrivals of customers are Poisson distributed with an average arrival rate of 2.44 per minute.a. What is the probability that at least 10 minutes will elapse between arrivals?b. What is the probability that at
During the summer at a small private airport in western Nebraska, the unscheduled arrival of airplanes is Poisson distributed with an average arrival rate of 1.12 planes per hour.a. What is the average interarrival time between planes?b. What is the probability that at least 2 hours will elapse
The exponential distribution can be used to solve Poisson-type problems in which the intervals are not time. The Airline Quality Rating Study published by the U.S. Department of Transportation reported that in a recent year, Airtran led the nation in fewest occurrences of mishandled baggage, with a
The Foundation Corporation specializes in constructing the concrete foundations for new houses in the South. The company knows that because of soil types, moisture conditions, variable construction, and other factors, eventually most foundations will need major repair. On the basis of its records,
During the dry month of August, one U.S. city has measurable rain on average only two days per month. If the arrival of rainy days is Poisson distributed in this city during the month of August, what is the average number of days that will pass between measurable rain? What is the standard
Data are uniformly distributed between the values of 6 and 14. Determine the value of f (x). What are the mean and standard deviation of this distribution? What is the probability of randomly selecting a value greater than 11? What is the probability of randomly selecting a value between 7 and 12?
Assume a normal distribution and find the following probabilities.a. P(x < 21 | µ = 25 and σ = 4).b. P(x ≥ 77 | µ = 50 and σ = 9).c. P(x > 47 | µ = 50 and σ = 6).d. P(13 < x < 29 | µ = 23 and σ = 4).e. P (x ≥ 105 | µ m = 90 and σ = 2.86).
Work the following binomial distribution problems by using the normal distribution. Check your answers by using Table A.2 to solve for the probabilities.a. P(x = 12 | n = 25 and p = .60).b. P(x > 5 | n = 15 and p = .50).c. P(x ≤ 3 | n = 10 and p = .50).d. P(x ≥ 8 | n = 15 and p = .40).
Find the probabilities for the following exponential distribution problems.a. P(x ≥ 3 | λ = 1.3).b. P(x < 2 | λ = 2.0).c. P(1 ≤ x ≤ 3 | λ = 1.65).d. P(x > 2 | λ = .405).
The U.S. Bureau of Labor Statistics reports that of persons who usually work full-time, the average number of hours worked per week is 43.4. Assume that the number of hours worked per week for those who usually work full-time is normally distributed. Suppose 12% of these workers work more than 48
A U.S. Bureau of Labor Statistics survey showed that one in five people 16 years of age or older volunteers some of his or her time. If this figure holds for the entire population and if a random sample of 150 people 16 years of age or older is taken, what is the probability that more than 50 of
An entrepreneur opened a small hardware store in a strip mall. During the first few weeks, business was slow, with the store averaging only one customer every 20 minutes in the morning. Assume that the random arrival of customers is Poisson distributed.a. What is the probability that at least one
In a recent year, the average price of a Microsoft Windows Upgrade was $90.28 according to PC Data. Assume that prices of the Microsoft Windows Upgrade that year were normally distributed, with a standard deviation of $8.53. If a retailer of computer software was randomly selected that year:a. What
According to the U.S. Department of Agriculture, Alabama egg farmers produce millions of eggs every year. Suppose egg production per year in Alabama is normally distributed, with a standard deviation of 83 million eggs. If during only 3% of the years Alabama egg farmers make over 2,655 million
The U.S. Bureau of Labor Statistics releases figures on the number of full-time wage and salary workers with flexible schedules. The numbers of full-time wage and salary workers in each age category are almost uniformly distributed by age, with ages ranging from 18 to 65 years. If a worker with a
A business convention holds its registration on Wednesday morning from 9:00 A.M. until 12:00 noon. Past history has shown that registrant arrivals follow a Poisson distribution at an average rate of 1.8 every 15 seconds. Fortunately, several facilities are available to register convention
M/PF Research, Inc. lists the average monthly apartment rent in some of the most expensive apartment rental locations in the United States. According to their report, the average cost of renting an apartment in Minneapolis is $951. Suppose that the standard deviation of the cost of renting an
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 say that their job is very stressful?c. What is
The U.S. Bureau of Economic Statistics reports that the average annual salary in the metropolitan Boston area is $50,542. Suppose annual salaries in the metropolitan Boston area are normally distributed with a standard deviation of $4,246. A Boston worker is randomly selected.a. What is the
Suppose interarrival times at a hospital emergency room during a weekday are exponentially distributed, with an average interarrival time of nine minutes. If the arrivals are Poisson distributed, what would the average number of arrivals per hour be? What is the probability that less than five
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 probability that a train will average less than 70
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 expect to increase the number of part-time jobs
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 probability that between 110 and 120 (inclusive)
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 period was 2.165 billion bushels. If the
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 when the head of the household has a college
According to the Polk Company, a survey of households using the Internet in 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 households who are using the Internet in buying
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 hurricanes during this season is Poisson
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 are of great assistance in the job marketplace. A recent Gallup survey found that 80% of Generation Xers considered
According to the Air Transport Association of America, the average operating cost of an MD-80 jet airliner is $2,087 per hour. Suppose the operating costs of an MD-80 jet airliner are normally distributed with a standard deviation of $175 per hour. At what operating cost would only 20% of the
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 the clerk has just checked out the last
In a recent year, the average daily circulation of The Wall Street Journal was 1,717,000. Suppose the standard deviation is 50,940. Assume the paper's daily circulation is normally distributed. On what percentage of days would circulation pass 1,800,000? Suppose the paper cannot support the fixed
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 between incoming calls? Two minutes?
Shown here is a Minitab output. Suppose the data represent the number of sales associates who are working in a department store in any given retail day. Describe the distribution including the mean and standard deviation. Interpret the shape of the distribution and the mean in light of the data
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 DistributionMean = 227 mg.Standard Deviation = 2.3 mg.x Value Probability < x Value220
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 DISTRIBUTION FUNCTIONNormal with mean = 2.35
A restaurant averages 4.51 customers per 10 minutes during the summer in the late afternoon. Shown here are Excel and Minitab output for this restaurant. Discuss the type of distribution used to analyze the data and the meaning of the probabilities.Exponential Distribution x Value
The Shell Oil Company, which began about 1912, had been for decades a household name as a quality oil company in the United States. However, by the late 1970s much of its prestige as a premiere company had disappeared. How could Shell regain its high status? In the 1990s, Shell undertook an
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.b. Conducting a telephone survey in Utica, New York, to determine the level of interest in opening a new hunting and fishing specialty store in the
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 customers. A sample of motels and hotels will be
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. Size of retail outlet (square feet).d. Geographic
If a company employs 3,500 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 frame for this study?
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 effects of petrochemical plants west of the
Give an example of how quota sampling could be used to conduct sampling by a company test marketing a new personal computer.
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 52b. Less than 51c. Less than 47d. Between 48.5 and 52.4e. Between 50.6 and 51.3
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 sample mean of more than 26.
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? Explain.
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?
Find the probability in each case.a. N = 1000, n = 60, µ = 75, and σ = 6; P(ẍ < 76.5) =?b. N = 90, n = 36, µ = 108, and σ = 3.46; P(107 < ẍ < 107.7) =?c. N = 250, n = 100, µ = 35.6, and σ = 4.89; P(ẍ ≥ 36) =?d. N = 5000, n = 60, µ = 125, and σ = 13.4; P(ẍ ≤ 123) =?
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 a researcher took a random sample of 38 people and
Suppose a subdivision on the southwest side of Denver, Colorado, contains 1,500 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 subdivision for all houses is $177,000, with a
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?
According to Nielsen Media Research, the average number of hours of TV viewing per household per week in the United States is 50.4 hours. Suppose the standard deviation is 11.8 hours and a random sample of 42 U.S. households is taken.a. What is the probability that the sample average is more than
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 p ≤ .21b. n = 33 and p > 7 .24c. n = 59 and .24 ≤ p < 6 .27d. n = 80 and p < 6 .30e. n = 800 and p < 6 .30
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 and .65?c. What is the probability that the
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? Discuss.
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?
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 are very close to the total limit on their
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 productive on Tuesdays?b. What is the probability
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 randomly selected.a. What is the probability that
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.b. A random sample of size 140 yielding 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 .53.b. The sample size is 458 and the sample
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%A researcher is conducting proportionate stratified random sampling with a sample size of 250. Approximately how many people should he sample
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 voters say they are committed to voting for her.
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 Pennsylvaniab. The average number of employees in all Alpha/Beta supermarkets in Californiac. A survey of commercial
A particular automobile costs an average of $17,755 in the Pacific Northwest. The standard deviation of prices is $650. Suppose a random sample of 30 dealerships in Washington and Oregon is taken, and their managers are asked what they charge for this automobile. What is the probability of getting
A company has 1,250 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.
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 $110. If the population variance is $525, what
A survey of 2,645 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 influence. Quality of product was the number one
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 manager. In addition, it asks questions
A researcher 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?
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.
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. Suppose 565 of these companies are
The average cost of a one-bedroom apartment in a town is $550 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 $530 if the population standard deviation is $100?
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, what is the probability that the sample
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 is taken.a. What is the probability that
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 of randomly sampling 140 women 16 years of
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 conducting a census? What are the trade-offs?
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