Assume that X is a Poisson random variable with μ = 15. Calculate the following probabilities. a. P (X ≤ 10) b. P (X = 13) c. P (X > 15) d. P (12 ≤ X ≤ 18)
> Find the probability that an Internal Revenue Service (IRS) auditor will catch only 4 income tax returns with illegitimate deductions if he randomly selects 5 returns from among 20 returns, of which 10 contain illegitimate deductions.
> A professor has learned that three students in her class of 20 will cheat on the exam. She decides to focus her attention on four randomly chosen students during the exam. a. What is the probability that she finds at least one of the students cheating? b
> Disturbing news regarding Scottish police concerns the number of crashes involving vehicles on operational duties (BBC News, March 10, 2008). Statistics showed that Scottish forces’ vehicles had been involved in traffic accidents at the rate of 1,000 per
> Suppose you draw three cards, without replacement, from a deck of well-shuffled cards. Remember that each deck consists of 52 cards, with 13 each of spades, hearts, clubs, and diamonds. a. What is the probability that you draw all spades? b. What is the
> The police have estimated that there are 12 major accidents per day on a particular 10-mile stretch of a national highway. Suppose the incidence of accidents is evenly distributed on this 10-mile stretch of the highway. a. Find the probability that there
> Despite the fact that home prices seem affordable and mortgage rates are at historic lows, real estate agents say they are showing more homes, but not selling more (The Boston Globe, March 7, 2009). A real estate company estimates that an average of five
> Studies have shown that bats can consume an average of ten mosquitoes per minute (berkshiremuseum.org). a. Calculate the average number of mosquitoes that a bat consumes in a 30-second interval. b. What is the probability that a bat consumes four mosquit
> According to a survey by consulting firm Watson Wyatt, approximately 19% of employers have eliminated perks or plan to do so in the next year (Kiplinger’s Personal Finance, February 2009). Suppose 30 employers are randomly selected. a. What is the probab
> Twenty percent of U.S. mortgages are “underwater” (The Boston Globe, March 5, 2009). A mortgage is considered underwater if the value of the home is less than what is owed on the mortgage. Suppose 100 mortgage holders are randomly selected. a. What is th
> Disturbing news regarding Scottish police concerns the number of crashes involving vehicles on operational duties (BBC News, March 10, 2008). Statistics showed that Scottish forces’ vehicles had been involved in traffic accidents at the rate of 1,000 per
> A random variable X follows the continuous uniform distribution with a lower bound of −2 and an upper bound of 4. a. What is the height of the density function f(x)? b. What are the mean and the standard deviation for the distribution? c. Calculate P(X ≤
> According to the Department of Transportation, 27% of domestic flights were delayed in 2007 (Money, May 2008). At New York’s John F. Kennedy Airport, five flights are randomly selected. a. What is the probability that all five flights are delayed? b. Wha
> Rent-to-own (RTO) stores allow consumers immediate access to merchandise in exchange for a series of weekly or monthly payments. The agreement is for a fixed time period. At the same time, the customer has the flexibility to terminate the contract by ret
> Discuss the factors that influence the margin of error for the confidence interval for the population mean. What can a practitioner do to reduce the margin of error?
> On a particularly busy section of the Garden State Parkway in New Jersey, police use radar guns to detect speeders. Assume the time that elapses between successive speeders is exponentially distributed with a mean of 15 minutes. a. Calculate the rate par
> A tollbooth operator has observed that cars arrive randomly at an average rate of 360 cars per hour. a. What is the mean time between car arrivals at this tollbooth? b. What is the probability that the next car will arrive within ten seconds?
> An investor owns a portfolio consisting of two mutual funds, A and B, with 35% invested in A. The following table lists the inputs for these funds. a. Calculate the expected value for the portfolio return. b. Calculate the standard deviation for the po
> A random variable X is exponentially distributed with a probability density function of f (x) = 5e−5x. Calculate the mean and the standard deviation of X.
> Entrance to a prestigious MBA program in India is determined by a national test where only the top 10% of the examinees are admitted to the program. Suppose it is known that the scores on this test are normally distributed with a mean of 420 and a standa
> Facing the worst economic climate since the dot-com bust in the early 2000s, high-tech companies in the United States search for investment opportunities with cautious optimism (USA TODAY, February 17, 2009). Suppose the investment team at Microsoft is c
> An analyst developed the following probability distribution for the rate of return for a common stock. a. Calculate the expected rate of return. b. Calculate the variance and the standard deviation of this probability distribution. Scenario Probabi
> The car speeds on a certain stretch of the interstate highway I-95 are known to be normally distributed with a mean of 72 and a standard deviation of 15. You have just heard a policeman comment that about 3% of the drivers drive at extremely dangerous sp
> A random variable X follows the continuous uniform distribution with a lower bound of 5 and an upper bound of 35. a. What is the height of the density function f(x)? b. What are the mean and the standard deviation for the distribution? c. Calculate P(X >
> A committee of 40 members consists of 24 men and 16 women. A subcommittee consisting of 10 randomly selected members will be formed. a. What are the expected number of men and women on the subcommittee? b. What is the probability that at least half of th
> According to figures released by the New York City government, smoking among New York City teenagers is on a decline, continuing a trend that began more than a decade ago (The New York Times, January 2, 2008). According to the New York City Youth Risk Be
> The National Science Foundation is fielding applications for grants to study climate change. Twenty universities apply for a grant, and only four of them will be awarded. If Syracuse University and Auburn University are among the 20 applicants, what is t
> David Barnes and his fiancée Valerie Shah are visiting Hawaii. There are 20 guests registered for orientation. It is announced that 12 randomly selected registered guests will receive a free lesson of Tahitian dance. a. What is the probability that both
> Many programming teams work independently at a large software company. The management has been putting pressure on these teams to finish a project on time. The company currently has 18 large programming projects, of which only 12 are likely to finish on
> Despite the repeated effort by the government to reform how Wall Street pays its executives, some of the nation’s biggest banks are continuing to pay out bonuses nearly as large as those in the best years before the crisis (The Washington Post, January 1
> A professor of management has heard that eight students in his class of 40 have landed an internship for the summer. Suppose he runs into three of his students in the corridor. a. Find the probability that none of these students has landed an internship.
> Suppose you have an urn of ten marbles, of which five are red and five are green. If you draw two marbles from this urn, what is the probability that both marbles are red? What is the probability that at least one of the marbles is red?
> Compute the probability of at least eight successes in a random sample of 20 items obtained from a population of 100 items that contains 25 successes. What are the expected number and the standard deviation of the number of successes?
> Assume that X is a hypergeometric random variable with N = 50, S = 20, and n = 5. Calculate the following probabilities. a. P (X = 2) b. P (X ≥ 2) c. P (X ≤ 3)
> Compute the probability of no successes in a random sample of three items obtained from a population of 12 items that contains two successes. What are the expected number and the standard deviation of the number of successes from the sample?
> Assume that X is a hypergeometric random variable with N = 15, S = 4, and n = 3. Calculate the following probabilities. a. P (X = 1) b. P (X = 2) c. P (X ≥ 2)
> An extended warranty is a prolonged warranty offered to consumers by the warranty administrator, the retailer, or the manufacturer. A report in The New York Times (November 23, 2009) suggests that 20.4% of laptops fail over three years. Roberto Dâ&
> A hospital administrator worries about the possible loss of electric power as a result of a power blackout. The hospital, of course, has a standby generator, but it, too, is subject to failure, having a mean time between failures of 500 hours. It is reas
> In the fiscal year that ended September 30, 2008, there were 24,584 age-discrimination claims filed with the Equal Employment Opportunity Commission, an increase of 29% from the previous year (The Wall Street Journal, March 7−8, 2009). Assume there were
> Due to the advent of tablets, American adults are watching significantly less television than they did in previous decades. In 2016, Nielsen reported that American adults are watching an average of five hours and four minutes, or 304 minutes, of televisi
> According to a government report, the aging of the U.S. population is translating into many more visits to doctors’ offices and hospitals (USA Today, August 7, 2008). It is estimated that an average person makes four visits a year to doctors’ offices and
> On average, 400 people are struck by lightning in the United States each year (The Boston Globe, July 21, 2008). a. What is the probability that at most 425 people are struck by lightning in a year? b. What is the probability that at least 375 people are
> Let Y have the lognormal distribution with mean 82.8 and variance 156.25. Compute the following probabilities. a. P (Y > 100) b. P (80 < Y < 100)
> Let Y = eX, where X is normally distributed. Compute the mean and the variance of X given the following information. a. μY = 14, σ2Y = 22 b. μY = 20, σ2Y = 22 c. μY = 20, σ2Y = 120
> Let Y = eX where X is normally distributed with μ = 1.8 and σ = 0.80. Compute the following values. a. P(Y ≤ 7.5) b. P(8 < Y < 9) c. The 90th percentile of Y
> Compute the mean and the variance of a lognormal variable Y = eX where X is normally distributed with the following mean and variance: a. μ = 3, σ2 = 2 b. μ = 5, σ2 = 2 c. μ = 5, σ2 = 3
> On average, there are 12 potholes per mile on a particular stretch of the state highway. Suppose the potholes are distributed evenly on the highway. a. Find the probability of finding fewer than two potholes in a quarter-mile stretch of the highway. b. F
> An economist reports that 560 out of a sample of 1,200 middle-income American households actively participate in the stock market. a. Construct the 90% confidence interval for the proportion of middle-income Americans who actively participate in the stoc
> Which of the following scenarios are likely to represent Poisson random variables? a. The number of violent crimes in New York over a six-week period. b. The number of customers of a bank manager who will default. c. The number of scratches on a 2-by-1-f
> Which of the following probabilities are likely to be found using a Poisson distribution? a. The probability that there will be six leaks in a specified stretch of a pipeline. b. The probability that at least 10 students in a class of 40 will land a job
> The mileage (in 1,000s of miles) that car owners get with a certain kind of radial tire is a random variable Y having a lognormal distribution such that Y = eX, where X is normally distributed. Let the mean and the standard deviation of the life of a rad
> On average, a certain kind of kitchen appliance requires repairs once every four years. Assume that the times between repairs are exponentially distributed. a. What is the probability that the appliance will work no more than three years without requirin
> The relief time provided by a standard dose of a popular children’s allergy medicine averages six hours with a standard deviation of two hours. a. Determine the percentage of children who experience relief for less than four hours if the relief time foll
> In a local law office, jobs to a printer are sent at a rate of 8 jobs per hour. Suppose that the number of jobs sent to a printer follows the Poisson distribution. a. What is the expected time between successive jobs? b. What is the probability that the
> Suppose that the average IQ score is normally distributed with a mean of 100 and a standard deviation of 16. a. What is the probability a randomly selected person will have an IQ score of less than 80? b. What is the probability that a randomly selected
> The length of components produced by a company is normally distributed with a mean of 6 cm and a standard deviation of 0.02 cm. Calculate the first, second, and third quartiles of the component length.
> The average household income in a community is known to be $80,000. Also, 20% of the households have an income below $60,000 and another 20% have an income above $90,000. Is it reasonable to use the normal distribution to model the household income in th
> In a CNNMoney.com poll conducted on July 13, 2010, a sample of 5,324 Americans were asked about what matters most to them in a place to live. Thirty-seven percent of the respondents felt job opportunities matter most. a. Construct the 90% confidence inte
> On St. Patrick’s Day, men spend an average of $43.87 while women spend an average of $29.54 (USA TODAY, March 17, 2009). Assume the standard deviations of spending for men and women are $3 and $11, respectively, and that both distributions are normally d
> The revised guidelines from the National High Blood Pressure Education Program define normal blood pressure as readings below 120/80 millimeters of mercury (The New York Times, May 14, 2003). Prehypertension is suspected when the top number (systolic) is
> A worker at a landscape design center uses a machine to fill bags with potting soil. Assume that the quantity put in each bag follows the continuous uniform distribution with low and high filling weights of 10 pounds and 12 pounds, respectively. a. Calcu
> It is well documented that a typical washing machine can last anywhere between 5 to 12 years. Let the life of a washing machine be represented by a lognormal variable, Y = eX, where X is normally distributed. In addition, let the mean and standard deviat
> Motorists arrive at a Gulf station at the rate of two per minute during morning hours. Assume that the arrival of motorists at the station follows a Poisson distribution. a. What is the probability that the next car’s arrival is in less than one minute?
> The Bahamas is a tropical paradise made up of 700 islands sprinkled over 100,000 square miles of the Atlantic Ocean. According to the figures released by the government of the Bahamas, the mean household income in the Bahamas is $39,626 and the median in
> Many U.S. households still do not have Internet access. Suppose 20 out of 80 households in a small southern town do not have Internet access. A company that provides high-speed Internet has recently entered the market. As part of the marketing campaign,
> Assume that X is a Poisson random variable with μ = 15. Calculate the following probabilities. a. P (X ≤ 10) b. P (X = 13) c. P (X > 15) d. P (12 ≤ X ≤ 18)
> Assume a Poisson random variable has a mean of four arrivals over a 10-minute interval. a. What is the mean of the random variable, defined by the time between arrivals? b. Find the probability that the next arrival would be within the mean time. c. Find
> Assume a Poisson random variable has a mean of 6 successes over a 120-minute period. a. Find the mean of the random variable, defined by the time between successes. b. What is the rate parameter of the appropriate exponential distribution? c. Find the pr
> The Gallup-Healthways Well-Being Index (www.well-beingindex.com) provides an assessment measure of health and well-being of U.S. residents. By collecting periodic data on life evaluation, physical health, emotional health, healthy behavior, work environm
> A certain brand of refrigerators has a length of life that is normally distributed with a mean and a standard deviation of 15 years and 2 years, respectively. a. What is the probability a refrigerator will last less than 6.5 years? b. What is the probabi
> A new car battery is sold with a two-year warranty whereby the owner gets the battery replaced free of cost if it breaks down during the warranty period. Suppose an auto store makes a net profit of $20 on batteries that stay trouble-free during the warra
> At the University of Notre Dame Mendoza College of Business, 40% of the students seeking a master’s degree specialize in finance (Kiplinger’s Personal Finance, March 2009). Twenty master’s degree students are randomly selected. a. What is the probability
> According to a report by the PEW Research Center, 85% of adults under 30 feel optimistic about the economy, but the optimism is shared by only 45% of those who are over 50 (Newsweek, September 13, 2010). A research analyst would like to construct 95% con
> An employee of the Bureau of Transportation Statistics has been given the task of estimating the proportion of on-time arrivals of a budget airline. A prior study had estimated this on-time arrival rate as 78.5%. What is the minimum number of arrivals th
> An economist would like to estimate the 95% confidence interval for the average real estate taxes collected by a small town in California. In a prior analysis, the standard deviation of real estate taxes was reported as $1,580. What is the minimum sample
> Suppose 40% of recent college graduates plan on pursuing a graduate degree. Fifteen recent college graduates are randomly selected. a. What is the probability that no more than four of the college graduates plan to pursue a graduate degree? b. What is th
> Research suggests that Americans make an average of 10 phone calls per day (CNN, August 26, 2010). Let the number of calls be normally distributed with a standard deviation of 3 calls. a. What is the probability that an average American makes between 4 a
> Linda Barnes has learned from prior studies that one out of five applicants gets admitted to top MBA programs in the country. She wishes to construct her own 90% confidence interval for the acceptance rate in top MBA programs. How large a sample should s
> A Monster.com poll of 3,057 individuals asked: “What’s the longest vacation you plan to take this summer?” The following relative frequency distribution summarizes the results. Response ……………………………………………………………………… Relative Frequency A few days ………………………
> A poll of 1,079 adults found that 51% of Americans support Arizona’s stringent new immigration enforcement law, even though it may lead to racial profiling (The New York Times/CBS News, April 28–May 2, 2010). Use the sample information to compute the 95%
> According to a survey of 1,235 businesses by IDC, a market-research concern in Framingham, Massachusetts, 12.1% of sole proprietors are engaging in e-commerce (The Wall Street Journal, July 26, 2007). a. With 95% confidence, what is the margin of error w
> Real estate investment in college towns continues to promise good returns (The Wall Street Journal, September 24, 2010). Marcela Treisman works for an investment firm in Michigan. Her assignment is to analyze the rental market in Ann Arbor, which is home
> A construction company in Naples, Florida, is struggling to sell condominiums. In order to attract buyers, the company has made numerous price reductions and better financing offers. Although condominiums were once listed for $300,000, the company believ
> The manager of a minor league baseball team wants to estimate the average fastball speed of two pitchers. He clocks 50 fastballs, in miles per hour, for each pitcher. A portion of the data is shown in the accompanying table. Pitcher 1 ………………………………………………
> Residents of Hawaii have the longest life expectancies, averaging 81.48 years (www.worldlifeexpectancy.com, data retrieved June 4, 2012). A sociologist collects data on the age at death for 50 recently deceased Michigan residents. A portion of the data i
> A realtor wants to estimate the mean price of houses in Mission Viejo, California. She collects a sample of 36 recent house sales (in $1,000s), a portion of which is shown in the accompanying table. Assume that the population standard deviation is 100 (i
> The following table shows the annual returns (in percent) for the Vanguard Energy Fund. Year …………………………………………………………………………………………… Return 2010 …………………………………………………………………………………………………. 13 2011 …………………………………………………………………………………………………. −2 2012 ………………………………………………
> A study by Allstate Insurance Co. finds that 82% of teenagers have used cell phones while driving (The Wall Street Journal, May 5, 2010). Suppose this study was based on a random sample of 50 teen drivers. a. Construct the 99% confidence interval for the
> The SAT is the most widely used test in the undergraduate admissions process. Scores on the math portion of the SAT are believed to be normally distributed and range from 200 to 800. A researcher from the admissions department at the University of New Ha
> Loans that are 60 days or more past due are considered seriously delinquent. The Mortgage Bankers Association reported that the rate of seriously delinquent loans has an average of 9.1% (The Wall Street Journal, August 26, 2010). Let the rate of seriousl
> In a sample of 30 observations, the number of successes equals 18. a. Construct the 88% confidence interval for the population proportion of successes. b. Construct the 98% confidence interval for the population proportion of successes. c. What happens t
> Students who graduated from college in 2010 owed an average of $25,250 in student loans (The New York Times, November 2, 2011). An economist wants to determine if average debt has changed. She takes a sample of 40 recent graduates and finds that their av
> Recently, six single-family homes in San Luis Obispo County in California sold at the following prices (in $1,000s): 549, 449, 705, 529, 639, and 609. a. Construct the 95% confidence interval for the mean sale price in San Luis Obispo County. b. What ass
> According to data from the Organization for Economic Cooperation and Development, the average U.S. worker takes 16 days of vacation each year (The Wall Street Journal, June 20, 2007). Assume that these data were based on a sample of 225 workers and that
> A hair salon in Cambridge, Massachusetts, reports that on seven randomly selected weekdays, the number of customers who visited the salon were 40, 30, 28, 22, 36, 16, and 50. It can be assumed that weekday customer visits follow a normal distribution. a.
> Over a 10-year sample period, the mean and the standard deviation of annual returns on a portfolio you are analyzing were 10% and 15%, respectively. You assume that returns are normally distributed. Construct the 95% confidence interval for the populatio
> A business student is interested in estimating the 99% confidence interval for the proportion of students who bring laptops to campus. He wishes a precise estimate and is willing to draw a large sample that will keep the sample proportion within five per
> Subprime lending was big business in the United States in the mid-2000s, when lenders provided mortgages to people with poor credit. However, subsequent increases in interest rates coupled with a drop in home values necessitated many borrowers to default
> On average, an American professional football game lasts about three hours, even though the ball is actually in play only 11 minutes (www.sportsgrid.com, January 14, 2014). Assume that game times are normally distributed with a standard deviation of 0.4
> Newscasters wish to estimate the proportion of registered voters who support the incumbent candidate in the mayoral election. In an earlier poll of 240 registered voters, 110 had supported the incumbent candidate. Find the sample size required to constru
> A budget airline wants to estimate what proportion of customers would consider paying $12 for in-flight wireless access. Given that the airline has no prior knowledge of the proportion, how many customers would it have to sample to ensure a margin of err
