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Business Statistics Contemporary Decision Making 6th Edition Ken Black - Solutions

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 Probability < x Value 220 0.0012 225
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
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?
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
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
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
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
Coastal businesses along the Gulf ofMexico 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
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
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 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
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)
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
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
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
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
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
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
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
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
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
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
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
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
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
Find the probabilities for the following exponential distribution problems. a. P(x31A 1.3) b. P(x2|A 2.0) C. P(1x31A 1.65) d. P(x2|A= .405)
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 5n 15 and p = .50) C. P(x3|n=10 and p = .50) d. P(x8n=15 and p = .40)
Assume a normal distribution and find the following probabilities. a. P(x < 21| 25 and = 4) b. P(x77|= 50 and = 9) c. P(x 47| = 50 and = 6) d. P(13
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?
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
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,
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
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
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
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, what
Determine the following exponential probabilities. a. P(x 51A 1.35) b. P(x 4|=1.7) d. P(x
Determine the mean and standard deviation of the following exponential distributions. a. A = 3.25 b. =0.7 c. A=1.1 d. A = 6.0
Use the probability density formula to sketch the graphs of the following exponential distributions. a. A=0.1 b. A=0.3 c. A=0.8 d. A = 3.0
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
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
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
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
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
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(x13 n = 20 and p = .60) = ? c.
Use the test m ; 3 to determine whether the following binomial distributions can be approximated by using the normal distribution. a. n = 8 and p = .50 b. n = 18 and p = .80 c. n = 12 and p = .30 d. n = 30 and p = .75 e. n = 14 and p = .50
Convert the following binomial distribution problems to normal distribution problems. Use the correction for continuity. b. a. P(x16 n = 30 and p = .70) P(10x20) | n = 25 and p = .50) c. P(x = 22|n 40 and p = .60) d. P(x 14 n = 16 and p = .45)
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?
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
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?
Suppose the standard deviation for Problem 6.7 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 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 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
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
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 average
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
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
Determine the probabilities for the following normal distribution problems. a. 604, or 56.8, x635 b. 48, or = 12, x < 20 c. 111, 33.8, 100 < x < 150 d. u 264, = 10.9, 250 < x < 255 37, or 4.35, x> 35 f. 156, = 11.4, x 170
Suppose the average U.S. household spends $2,100 a year on all types of insurance.Suppose the figures are uniformly distributed between the values of $400 and $3,800.What are the standard deviation and the height of this distribution? What proportion of households spends more than $3,000 a year on
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 of
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
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) = ?6.2 x is uniformly distributed over a
Study the Minitab graph. Discuss the distribution including type, shape, and probability outcomes. Probability Poisson Distribution: Lambda = 1.784 0.3 0.2 0.1 0.0 0 5 10
Study the graphical output from Excel. Describe the distribution and explain why the graph takes the shape it does. Hobability 0.2 0.18 0.16 0.14 0.12 0.11 0.08 0.06 0.04 0.02 Binomial Distribution: n = 22 and p = .64 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 x Values
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: = 2.78 0 1 0.0620 0.1725 2 0.2397 134 0.2221 4 0.1544 5 0.0858 6 0.0398 7 0.0158 8 0.0055 9 0.0017 10 0.0005 11 0.0001
Study the Minitab output. Discuss the type of distribution, the mean, standard deviation, and why the probabilities fall as they do. Probability Density Function Binomial with n = 15 and n = 0.36 0 1 XOL234567 P (X = x) 0.001238 0.010445 0.041128 0.100249 0.169170 0.209347 0.196263 0.141940
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 2.92 serious actions per 1,000 doctors. The state with the lowest number was South Carolina, with
In one midwestern 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 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.a. If five different universities are selected randomly from the list, what is the probability that three of them have enrollments of
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
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
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 are
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 rate of 2.4 calls per minute.a. If an
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
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 Audit Bureau of Circulations, the top 25 city newspapers in the United States ranked according to circulation are:Suppose a researcher wants to sample a portion of these newspapers and compare the sizes of the business sections of the Sunday papers. She randomly samples eight of
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
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 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
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
According to Padgett Business Services, 20% of all smallbusiness 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 the
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
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.
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 more than three defects, the buyer will reject
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 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
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 probability that x 2?
Use Table A.3, Appendix A, to find the following Poisson distribution values.a. P(x = 3 l = 1.8)b. P(x 5 l = 3.3)c. P(x 3 l = 2.1)d. P(2 x 5 l = 4.2)
Use the Poisson formula to solve for the probabilities of the following Poisson distribution problems.a. If l = 1.25, what is the probability that x = 4?b. If l = 6.37, what is the probability that x 1?c. If l = 2.4, what is the probability that x 5?
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 7 20 ƒ 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, what is the probability that x 7?d. If n = 14 and
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
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 three of the computers. The purchasing company can detect the defective wiring.What is the probability that the purchasing company
Shown here are the top 10 U.S. cities ranked by number of rooms sold in a recent year.Rank City Number of Rooms Sold 1 Las Vegas (NV) 40,000,000 2 Orlando (FL) 27,200,000 3 Los Angeles (CA) 25,500,000 4 Chicago (IL) 24,800,000 5 New York City (NY) 23,900,000 6 Washington (DC) 22,800,000 7 Atlanta
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
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
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 that
Compute the following probabilities by using the hypergeometric 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
A high percentage of people who fracture or dislocate a bone see a doctor for that condition. Suppose the percentage is 99%. Consider a sample in which 300 people are randomly selected who have fractured or dislocated a bone.a. What is the probability that exactly five of them did not see a
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.
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

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