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Business Statistics For Contemporary Decision Making 8th Edition Black Ken - Solutions
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) account less than $5, 000 opt to take their
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
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
Find the following values by using the Poisson formula.a. P (x = 5 | l = 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 < 8 | λ = 4.4)
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)
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 = 6.3b. λ = 1.3c. λ = 8.9d. λ = 0.6 Discuss.
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
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.
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
Ship collisions in the Houston Ship Channel are rare. Suppose the numbers 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
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 a
A medical researcher estimates that .00004 of the population has a rare blood disorder. If the researcher randomly selects 100, 000 people from the population,a. What is the probability that seven or more people will have the rare blood disorder?b. What is the probability that more than 10 people
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 six or more pages contain errors?b. What is the probability that more than 10 pages contain errors?c.
Compute the following probabilities by using the hyper-geometric formula.a. The probability of x = 3 if N = 11, A = 8, and n = 4b. The probability of x < 2 if N = 15, A = 5, and n = 6c. The probability of x = 0 if N = 9, A = 2, and n = 3d. The probability of x > 4 if N = 20, A = 5, and n = 7
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 six companies are randomly selected.a. What is the probability that exactly one company is privately owned?b. What is the probability
Catalog Age lists the top 17 U.S. firms in annual catalog sales. Dell Computer is number one followed by IBM and W.W. Grainger. Of the 17 firms on the list, 8 are in some type of computer-related business. Suppose four firms are randomly selected.a. What is the probability that none of the firms is
W. Edwards Deming in his red bead experiment had a box of 4, 000 beads, of which 800 were red and 3,200, 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 4 are red and 16 are white. This experiment
Shown here are the top 10 U.S. cities ranked by number of hotel rooms sold in a recent year.Suppose four of these cities are selected randomly.a. What is the probability that exactly two cities are in California?b. What is the probability that none of the cities is east of the Mississippi River?c.
A company produces and ships 16 personal computers knowing that four of them have defective wiring. The company that purchased the computers is going to thoroughly test three of the computers. The purchasing company can detect the defective wiring. What is the probability that the purchasing
A western city has 18 police officers eligible for promotion. Eleven of the 18 are Hispanic. Suppose only five of the police officers are chosen for promotion and that one is Hispanic. If the officers chosen for promotion had been selected by chance alone, what is the probability that one or fewer
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, what is the probability that x > 7?d. If n =
Use Table A.2, Appendix A, to find the values of the following binomial distribution problems.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)
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 > 5?
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)
Solve the following problems by using the hyper-geometric 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 probability that x ≥ 2?
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 is taken.a. What is the probability that
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 probability that three cars will arrive to use the diesel
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. Suppose an inspector randomly samples a
Suppose that, for every lot of100 computer chips a company produces, an average of 1.4 is 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 more than three defects, the buyer will reject all
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 conditions in your state promote healthy hearts.
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 said they thought seriously about quitting
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. Nineteen percent say having a good plan is
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. What is the probability that exactly five
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 actually occurred, what would be some of the
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 and if a researcher randomly selects 25 U.S.
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 is true for all women and if a woman is
According to the Audit Bureau of Circulations, the top 25 city newspapers in the United States ranked according to circulation are:Rank .......Newspaper1 .......New York Times (NY)2 .......Los Angeles Times (CA)3 .......San Jose Mercury News (CA)4 .......Washington Post (DC)5 .......New York Daily
An office in Albuquerque has 24 workers including management. Eight of the workers commute to work from the west side of the Rio Grande River. Suppose six of the office workers are randomly selected.a. What is the probability that all six workers commute from the west side of the Rio Grande?b. What
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 the mean and the standard deviation for this
One of the earliest applications of the Poisson distribution was in analyzing incoming calls to a telephone switch-board. Analysts generally believe that random phone calls are Poisson distributed. Suppose phone calls to a switch-board arrive at an average rate of 2.4 calls per minute.a. If an
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. What is the probability that eight or more
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 1, 000 billings are randomly sampled by an auditor.a. What is the probability
The following table lists the 25 largest U.S. universities according to enrollment figures from The World Almanac. The state of location is given in parentheses.University ................ EnrollmentUniversity of Phoenix (AZ) ......... 292, 797Arizona State University (AZ) ........ 68, 064Ohio
In one mid-western city, the government has 14 repossessed houses, which are evaluated to be worth about the same. 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 four of the houses. Which houses the contractor will
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 3.05 serious actions per 1000 doctors. The state with the lowest number was Minnesota with only
Study the Excel output. Explain the distribution in terms of shape and mean. Are these probabilities what you would expect? Why or why not? x Values ..... Poisson Probabilities: λ = 2.780 ....... 0.06201 ....... 0.17252 ....... 0.23973 ....... 0.22214 ....... 0.15445 ....... 0.08586
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 want to sue your company for discriminatory hiring
Study the Minitab output. Discuss the type of distribution, the mean, standard deviation, and why the probabilities fall as theydo.
Study the graphical output from Excel. Describe the distribution and explain why the graph takes the shape itdoes.
Study the Minitab graph. Discuss the distribution including type, shape, and probabilityoutcomes.
Over three decades ago, four business people who had experience in retailing natural foods through food stores believed that there was a demand for a supermarket for natural foods. As a result, in 1980 in Austin, Texas, they founded the first Whole Foods Market store in a building that had around
Values are uniformly distributed between 200 and 240.a. What is the value of f (x) for this distribution?b. Determine the mean and standard deviation of this distribution.c. Probability of (x > 230) =?d. Probability of (205 ≤ x ≤ 220) =?e. Probability of (x ≤ 225) =?
x is uniformly distributed over a range of values from 8 to 21.a. What is the value of f (x) for this distribution?b. Determine the mean and standard deviation of this distribution.c. Probability of (10 ≤ x < 17) =?d. Probability of (x < 22) =?e. Probability of (x ≥ 7) =?
The retail price of a medium-sized box of a well-known brand of cornflakes ranges from $2.80 to $3.14.Assume these prices are uniformly distributed. What are the average price and standard deviation of prices in this distribution? If a price is randomly selected from this list, what is the
The average fill volume of a regular can of soft drink is 12 ounces. Suppose the fill volume of these cans ranges from 11.97 to 12.03 ounces and is uniformly distributed. What is the height of this distribution? What is the probability that a randomly selected can contains more than 12.01 ounces
According to the U.S. Department of Labor, the average American household spends $639 on household supplies per year. Suppose annual expenditures on household supplies per household are uniformly distributed between the values of $253 and $1,025.What are the standard deviation and the height of
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 $73.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 cell phone bill is more than
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
Tool workers 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)
Based on annual driving of 15,000 miles and fuel efficiency of 20 mpg, a car in the United States uses, on average, 750 gallons of gasoline per year. If annual automobile fuel usage is normally distributed and if 29.12% of cars in the United States use less than 500 gallons of gasoline per year,
The U.S. national average door-to-doctor wait time for patients to see a doctor is now 21.3 minutes. Suppose such wait times are normally distributed with a standard deviation of 6.7 minutes. Some patients will have to wait much longer than the mean to see the doctor. In fact, based on this
Suppose commute times in a large city are normally distributed and that 62.5% of commuters in this city take more than 21 minutes to commute one-way. If the standard deviation of such commutes is 6.2 minutes, what is the mean commute?
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 µ ± 3σ 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
According to ars technica, HP is the leading company in the United States in PC sales with about 27% of the market share. Suppose a business researcher randomly selects 130 recent purchasers of PCs in the United States.a. What is the probability that more than 39 PC purchasers bought an HP
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 Discuss.
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 inter arrival 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 Air Travel Consumer Report 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 rains? What is the standard
Data are uniformly distributed between the values of 6 and 14.Determine the value of f (x).What is 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 = 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
According to an NRF survey conducted by BIG research, the average family spends about $237 on electronics (computers, cell phones, etc.) in back-to-college spending per student. Suppose back-to-college family spending on electronics is normally distributed with a standard deviation of $54. If a
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 produce more than 2,655
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.If60 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 inter-arrival times at a hospital emergency room during a weekday are exponentially distributed, with an average inter-arrival 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
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