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 > 10).
> Construct the null and the alternative hypotheses for the following claims: a. “I am going to get the majority of the votes to win this election.” b. “I suspect that your 10-inch pizzas are, on average, less than 10 inches in size.” c. “I will have to fi
> A politician claims that he is supported by a clear majority of voters. In a recent survey, 24 out of 40 randomly selected voters indicated that they would vote for the politician. Is the politician’s claim justified at the 5% level of significance?
> Research shows that many banks are unwittingly training their online customers to take risks with their passwords and other sensitive account information, leaving them more vulnerable to fraud (Yahoo.com, July 23, 2008). Even web-savvy surfers could find
> In order to endure financial hardships such as unemployment and medical emergencies, Americans have increasingly been raiding their already fragile retirement accounts (MSN Money, July 16, 2008). It is reported that between 1998 and 2004, about 12% of fa
> A study by Allstate Insurance Co. finds that 82% of teenagers have used cell phones while driving (The Wall Street Journal, May 5, 2010). In October 2010, Massachusetts enacted a law that forbids cell phone use by drivers under the age of 18. A policy an
> You would like to determine if more than 50% of the observations in a population are below 10. At α = 0.05, conduct the test on the basis of the following 20 sample observations: 8 12 14 11 7 8 12 6 8 9 6 11 4 13 10 3. LO
> You would like to determine if the population probability of success differs from 0.70. You find 62 successes in 80 binomial trials. Implement the test at the 1% level of significance.
> In order to test if the population proportion is greater than 0.65, you draw a random sample of 200 observations and obtain a sample proportion of 0.72. a. Specify the competing hypotheses. b. Is the normality condition satisfied? Explain. c. Calculate t
> In order to conduct a hypothesis test for the population proportion, you sample 320 observations that result in 128 successes. Conduct the following tests at α = 0.05. a. H0: p ≥ 0.45; HA: p < 0.45 b. H0: p = 0.45; HA: p ≠ 0.45
> A recent survey asked 5,324 individuals: What’s most important to you when choosing where to live? The responses are shown by the following frequency distribution. Response ……………………………………………………………………………………. Frequency Good jobs ……………………………………………………………………
> In order to test if the population proportion differs from 0.40, you draw a random sample of 100 observations and obtain a sample proportion of 0.48. a. Specify the competing hypotheses. b. Is the normality condition satisfied? Explain. c. Calculate the
> The data accompanying this exercise show miles per gallon (MPG). a. State the null and the alternative hypotheses in order to test whether the average MPG differs from 95. b. Calculate the value of the test statistic and the p-value. c. At α = 0.05, can
> Construct the null and the alternative hypotheses for the following tests: a. Test if the mean weight of cereal in a cereal box differs from 18 ounces. b. Test if the stock price increases on more than 60% of the trading days. c. Test if Americans get an
> A mortgage specialist would like to analyze the average mortgage rates for Atlanta, Georgia. He collects data on the annual percentage rates (APR in %) for 30-year fixed loans as shown in the following table. If he is willing to assume that these rates a
> A car manufacturer is trying to develop a new sports car. Engineers are hoping that the average amount of time that the car takes to go from 0 to 60 miles per hour is below 6 seconds. The manufacturer tested 12 of the cars and clocked their performance t
> A machine that is programmed to package 1.20 pounds of cereal in each cereal box is being tested for its accuracy. In a sample of 36 cereal boxes, the mean and the standard deviation are calculated as 1.22 pounds and 0.06 pound, respectively. a. Set up t
> Consider the following hypotheses: The population is normally distributed. A sample produces the following observations: Conduct the test at the 1% level of significance. H6 μ 2 100 На и < 100 95 99 85 80 98 97
> Consider the following hypotheses: The population is normally distributed. A sample produces the following observations: Conduct the test at the 5% level of significance. Ho: ju = 8 μ Hi fH # 8 A- 6 9 8 7 7 11 10
> Body mass index (BMI) is a reliable indicator of body fat for most children and teens. BMI is calculated from a child’s weight and height and is used as an easy-to-perform method of screening for weight categories that may lead to healt
> Consider the following hypotheses: a. A sample of 25 observations yields a sample mean of −12. Assume that the sample is drawn from a normal population with a sample standard deviation of 4. b. Calculate the value of the test statisti
> In order to conduct a hypothesis test for the population mean, a random sample of 24 observations is drawn from a normally distributed population. The resulting sample mean and sample standard deviation are calculated as 4.8 and 0.8, respectively. Conduc
> In order to test if the population mean differs from 16, you draw a random sample of 32 observations and compute the sample mean and the sample standard deviation as 15.2 and 0.6, respectively. Conduct the test at the 1% level of significance.
> Consider the following hypotheses: A sample of 16 observations yields a sample mean of 46. Assume that the sample is drawn from a normal population with a sample standard deviation of 10. a. Calculate the value of the test statistic. b. At the 5% signi
> An economist wants to test if the average hourly wage is less than $22. Assume that the population standard deviation is $6. a. State the null and the alternative hypotheses for the test. b. The data accompanying this exercise show hourly wages. Find the
> The data accompanying this exercise show the weekly stock price for Home Depot. Assume that stock prices are normally distributed with a population standard deviation of $3. a. State the null and the alternative hypotheses in order to test whether or not
> According to the Centers for Disease Control and Prevention (February 18, 2016), 1 in 3 American adults don’t get enough sleep. A researcher wants to determine if Americans are sleeping less than the recommended 7 hours of sleep on weekdays. He takes a r
> A committee of 10 is to be chosen from 50 people, 25 of whom are Republicans and 25 Democrats. The committee is chosen at random. a. What is the probability that there will be five Republicans and five Democrats? b. What is the probability that a majorit
> 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 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
> 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)
> 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
