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Questions and Answers of Statistics

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
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
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
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 =
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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 ≤
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
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
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.
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
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
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
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
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
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
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
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
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
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
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?
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.
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
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
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
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
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
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
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
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
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)
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
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
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
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
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 =
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
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
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
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.
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
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
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
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
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
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
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 =
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.
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
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
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
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
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
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
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 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
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
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
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
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
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
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 |
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
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
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
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
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
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
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
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
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
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
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
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,
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

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