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Question: The following table lists the 15 largest

The following table lists the 15 largest U.S. universities according to enrollment in a recent year.
The following table lists the 15 largest U.S. universities according to enrollment in a recent year.

a) If five different universities are selected randomly from the list, what is the probability that exactly three of them have enrollments of more than 50,000?
b) If eight different universities are selected randomly from the list, what is the probability that two or fewer are universities in Florida?
c) Suppose universities are being selected randomly from this list with replacement. If five universities are sampled, what is the probability that the sample will contain exactly two universities in Texas?

a) If five different universities are selected randomly from the list, what is the probability that exactly three of them have enrollments of more than 50,000? b) If eight different universities are selected randomly from the list, what is the probability that two or fewer are universities in Florida? c) Suppose universities are being selected randomly from this list with replacement. If five universities are sampled, what is the probability that the sample will contain exactly two universities in Texas?





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Rank University 1 Texas A&M 2 University of Central Florida 3 Ohio State University 4 Arizona State University 5 The University of Texas 6 University of Minnesota 7 University of Florida 8 State Enrollment TX 63,813 FL 62,953 OH 58,663 AZ 51,984 TX 50,950 MN 50,678 FL 50,645 Michigan State University ΜΙ 50,538 University of Maryland MD 50,248 10 New York University NY 11 Florida International University FL 12 Rutgers University NJ 13 Indiana University IN 14 PA Penn State University 15 University of Illinois IL a 50,027 49,782 49,428 48,514 47,307 45,842


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> 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

> 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)

> 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 r

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> Shown here is a graph of a binomial distribution for n = 6. Study the graph and from the graph, estimate what you think is the mean of this distribution. Approximately what do you think is the value of p and why? 0.45 0.4 0.35 0.3 0.25 0.2 - 0.15 0.1

> 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, Spirit Airlines led the nation

> 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 p

> 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

> 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

> 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

> 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)

> Determine the mean and standard deviation of the following exponential distributions. a) λ = 3.25 b) λ = 0.7 c) λ = 1.1 d) λ = 6.0

> Use the probability density formula to sketch the graphs of the following exponential distributions. a) λ = 0.1 b) λ = 0.3 c) λ = 0.8 d) λ = 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

> According to the International Data Corporation, HP is the leading company in the United States in PC sales with about 23% of the market share. Suppose a business analyst randomly selects 130 recent purchasers of PCs in the United States. a) What is the

> Use the probability tables in Table A.2 and sketch the graph of each of the following binomial distributions. Note on the graph where the mean of the distribution falls. Table A.2&acirc;&#128;&#148;and cumulating the values&acirc;&#128;&#148;we have the

> 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 ca

> 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 t

> 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

> 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) Pro

> 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)

> 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 = .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. 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

> According to one source, the average cumulated college student loan debt for a graduating senior is $29,400. Assume that such debt is normally distributed and that the standard deviation is $5,684. Thirty percent of these graduating seniors owe more than

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> Solve for the mean and standard deviation of the following binomial distributions. a) n = 20 and p = .70 b) n = 70 and p = .35 c) n = 100 and p = .50

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> 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. Expo

> Study the Minitab graph. Discuss the distribution including type, shape, and probability outcomes. Probability 0.3 0.2 0.1 0.0 0 Poisson Distribution: Lambda = 1.784 5 x Values 10

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> 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 1000 billings are randomly sampled

> 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

> 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

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> An office in Albuquerque has 24 workers including management. Eight of the workers commute to work from the west side of the Rio Grande. Suppose 6 of the office workers are randomly selected. a) What is the probability that all 6 workers commute from the

> According to the Audit Bureau of Circulations, the top 25 city newspapers in the United States ranked according to circulation are: Rank ____________________ Newspaper 1 …………..………………………… New York Times (NY) 2 …………………………..……… Los Angeles Times (CA) 3 …………

> Solve the following problems by using the binomial formula. a) If n = 4 and p = .10, find P(x = 3). b) If n = 7 and p = .80, find P(x = 4). c) If n = 10 and p = .60, find P(x ≥ 7). d) If n = 12 and p = .45, find P(5 ≤ x ≤ 7).

> 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

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> 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.

> 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 s

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> 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 probabilit

> 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)

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> Use Table A.2, Appendix A, to find the values of the following binomial distribution problems. Table A.2: 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)

> Solve for the probabilities of the following binomial distribution problems by using the binomial formula. a) If n = 11 and p = .23, what is the probability that x = 4? b) If n = 6 and p = .50, what is the probability that x ≥ 1? c) If n = 9 and p = .85,

> A western city has 18 police officers eligible for promotion. Eleven of the 18 are Hispanic. Suppose only 5 of the police officers are chosen for promotion and that 1 is Hispanic. If the officers chosen for promotion had been selected by chance alone, wh

> A company produces and ships 16 personal computers knowing that 4 of them have defective wiring. The company that purchased the computers is going to thoroughly test 3 of the computers. The purchasing company can detect the defective wiring. What is the

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> W. Edwards Deming in his red bead experiment had a box of 4000 beads, of which 800 were red and 3200 were white. * Suppose a researcher were to conduct a modified version of the red bead experiment. In her experiment, she has a bag of 20 beads, of which

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> The Fortune 500 includes the top 20 U.S. companies by revenue. Walmart is number one followed by Exxon Mobil and Berkshire Hathaway. Of the 20 companies on the list, 5 are in some type of healthcare-or pharmaceutical-related business. Suppose 3 firms are

> Shown here are the top 19 companies in the world in terms of oil refining capacity. Some of the companies are privately owned and others are state owned. Suppose 6 companies are randomly selected. a) What is the probability that exactly 1 company is priv

> Compute the following probabilities by using the hypergeometric formula. a) The probability of x = 3 if N = 11, A = 8, and n = 4 b) The probability of x < 2 if N = 15, A = 5, and n = 6 c) The probability of x = 0 if N = 9, A = 2, and n = 3 d) The probabi

> A data firm records a large amount of data. Historically, .9% of the pages of data recorded by the firm contain errors. If 200 pages of data are randomly selected, a) What is the probability that 6 or more pages contain errors? b) What is the probability

> A medical researcher estimates that .00004 of the population has a rare blood disorder. a) If the researcher randomly selects 100,000 people from the population, what is the probability that 7 or more people will have the rare blood disorder? b) If the r

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> Sketch the graphs of the following Poisson distributions. Compute the mean and standard deviation for each distribution. Locate the mean on the graph. Note how the probabilities are graphed around the mean. a) λ = 6.3 b) λ = 1.3 c) λ = 8.9 d) λ = 0.6

> Find the following values by using the Poisson tables in Appendix A. a) P(x = 6│λ = 3.8) b) P(x > 7│λ = 2.9) c) P(3 ≤ x ≤ 9│λ = 4.2) d) P(x = 0│λ = 1.9) e) P(x ≤ 6│λ = 2.9) f) P(5 < x < 8│λ = 5.7

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