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).
> 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
> 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 m
> 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 nee
> 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—and cumulating the values—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
> 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?
> 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 s
> 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
> 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
> 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?
> 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 below 17% of the values. c)
> 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
> 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) Probabilit
> 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
> Study the graphical output from Excel. Describe the distribution and explain why the graph takes the shape it does. Probability 0.2 0.18 0.16- 0.14 0.12 0.1 0.08- 0.06- 0.04- 0.02- 0 Binomial Distribution: n = 22 and p = .64 0 1 2 3 4 5 6 7 8 9 10 11
> 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: 0 …………………………………………… 0.0620 1 ……….…………………………………… 0.1725 2 ………………………………
> Study the Minitab output. Discuss the type of distribution, the mean, the standard deviation, and why the probabilities fall as they do. Probability Density Function Binomial with n = 15 and n = 0.38 x …………………………. P(X = () 0 ………………………. 0.001238 1 …………………
> Solve the following problems by using the binomial tables (Table A.2). Table A.2 — and cumulating the values—we have the following probability of x ≤ 2 for each value of p and the expected value (&I
> 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 around 3.00 serious actions per 1000 doctors. A 2016 stu
> In one Midwestern city, the government has 14 repossessed houses, which are evaluated to be worth about the same amount. 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 4 o
> 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
> 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 wants
> 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
> 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
> 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 …………
> 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
> 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
> 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 a
> 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)
> 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
> 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 con
> 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 mor
> 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 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 probabilit
> Suppose 20% of the people in a city prefer Pepsi-Cola as their soft drink of choice. If a random sample of six people is chosen, the number of Pepsi drinkers could range from zero to six. Shown here are the possible numbers of Pepsi drinkers in a sample
> 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 i
> 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)
> 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 >
> 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
> Shown here are the top 10 U.S. cities ranked by population. Suppose four of these cities are randomly selected. a) What is the probability that exactly two cities are in California? b) What is the probability that none of these cities is east of the Mis
> 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
> The following data are the result of a historical study of the number of flaws found in a porcelain cup produced by a manufacturing firm. Use these data and the associated probabilities to compute the expected number of flaws and the standard deviation o
> 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
> 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
> Ship collisions in the Houston Ship Channel are rare. Suppose the number 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
> 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
> 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 5 minutes from 7 P.M. until 8 P.
> On Monday mornings, the First National Bank has only 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 mo
> Determine the mean, the variance, and the standard deviation of the following discrete distribution. x __________________ P(x) 0 ………………………………………… .103 1 …….…………………………………… .118 2 ………………………………………… .246 3 ………………………………………… .229 4 ………………………………………… .138 5 …………
> 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
> 1. Whole Foods Market has shown steady growth at a time when traditional supermarkets have been flat. This could be attributed to a growing awareness of and demand for more natural foods. According to a study by Mintel in 2006, 30% of consumers have a hi
> 1. 3M has developed a composite measure, a 3M™ Value Index Score, which provides a standard metric to assess accountable value in healthcare. This index score is a composite measure based on six critical primary care domains derived from 16 measures of k
> 1. According to the National Association of Insurance Commissioners (NAIC), the average premium for homeowner’s insurance in the United States in a recent year was $1,034. Suppose these premium rates are uniformly distributed across the country from $535
> 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 effec
> If a company employs 3500 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
> If every 11th item is systematically sampled to produce a sample size of 75 items, approximately how large is the population?
> A city’s telephone book lists 100,000 people. If the telephone book is the frame for a study, how large would the sample size be if systematic sampling were done on every 200th person?
> According to Runzheimer International, a typical business traveler spends an average of $281 per day in Chicago. This cost includes hotel, meals, car rental, and incidentals. A survey of 65 randomly selected business travelers who have been to Chicago on
> Give a variable that could be used to stratify the population for each of the following studies. List at least four subcategories for each variable. a) A political party wants to conduct a poll prior to an election for the office of U.S. senator in Minne
> Find the following values by using the Poisson formula. a) P(x = 5│λ = 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
> 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) Siz
> The U.S. Bureau of Labor Statistics released hourly wage figures for various countries for workers in the manufacturing sector. The hourly wage was $30.67 for Switzerland, $20.20 for Japan, and $23.82 for the United States. Assume that in all three count
> In a particular area of the Northeast, an estimated 75% of the homes use heating oil as the principal heating fuel during the winter. A random telephone survey of 150 homes is taken in an attempt to determine whether this figure is correct. Suppose 120 o
> 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 conduc
> 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
> 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 i
