You are considering the risk-return profile of two mutual funds for investment. The relatively risky fund promises an expected return of 8% with a standard deviation of 14%. The relatively less risky fund promises an expected return and standard deviation of 4% and 5%, respectively. Assume that the returns are approximately normally distributed. a. Which mutual fund will you pick if your objective is to minimize the probability of earning a negative return? b. Which mutual fund will you pick if your objective is to maximize the probability of earning a return above 8%?
> A variety of packaging solutions exist for products that must be kept within a specific temperature range. Cold chain distribution is particularly useful in the food and pharmaceutical industries. A packaging company strives to maintain a constant temper
> American workers are increasingly planning to delay retirement (U.S. News & World Report, June 30, 2010). According to a Pew Research Center comprehensive survey, 35% of employed adults of age 62 and older say they have pushed back their retirement date.
> In the previous question regarding walking regimens of the residents of Miami, explain how you can obtain a representative sample based on the following sampling strategies: Data from Problem 51: A seminal study conducted by scientists at the Universit
> A seminal study conducted by scientists at the University of Illinois found evidence of improved memory and reasoning for those who took three vigorous 40-minute walks a week over six months (Newsweek, June 28–July 5, 2010). As an assistant manager worki
> Following customer complaints about the quality of service, Dell stopped routing corporate customers to a technical support call center in Bangalore, India (USA TODAY, November 24, 2003). Suppose Dell’s decision to direct customers to call centers outsid
> In the previous question regarding Vons’ store hours, explain how you can obtain a representative sample based on the following sampling strategies: Previous question: Vons, a large supermarket in Grover Beach, California, is considering extending its
> Random samples of size n = 36 are taken from a population with mean μ = 150 and standard deviation σ = 42. a. Construct the centerline and the upper and lower control limits for the chart. b. Suppose five samples of size 36 produced the following sample
> Random samples of size n = 25 are taken from a normally distributed population with mean μ = 20 and standard deviation σ = 10. a. Construct the centerline and the upper and lower control limits for the chart. b. Suppose six samples of size 25 produced th
> Vons, a large supermarket in Grover Beach, California, is considering extending its store hours from 7:00 am to midnight, seven days a week, to 6:00 am to midnight. Discuss the sampling bias in the following sampling strategies: a. Mail a prepaid envelop
> Random samples of size n = 250 are taken from a population with p = 0.04. a. Construct the centerline and the upper and lower control limits for the chart. b. Repeat the analysis with n = 150. c. Discuss the effect of the sample size on the control limit
> A random sample of 24 observations is used to estimate the population mean. The sample mean and the sample standard deviation are calculated as 104.6 and 28.8, respectively. Assume that the population is normally distributed. a. Construct the 90% confide
> Consider a normally distributed population with mean μ = 80 and standard deviation σ = 14. a. Construct the centerline and the upper and lower control limits for the chart if samples of size 5 are used. b. Repeat the analysis with samples of size 10. c.
> It is expected that only 60% in a graduating class of 250 will find employment in the first round of a job search. You have 20 friends who have recently graduated. a. Discuss the sampling distribution of the sample proportion of your friends who will fin
> Suppose in the previous question that the analyst had randomly chosen 12 CEO compensations for 2006. a. Is it necessary to apply the finite population correction factor? Explain. b. Is the sampling distribution of the sample mean approximately normally d
> Natalie Min is an undergraduate in the Haas School of Business at Berkeley. She wishes to pursue an MBA from Berkeley and wants to know the profile of other students who are likely to apply to the Berkeley MBA program. In particular, she wants to know th
> After years of rapid growth, illegal immigration into the United States has declined, perhaps owing to the recession and increased border enforcement by the United States (Los Angeles Times, September 1, 2010). While its share has declined, California st
> At a new exhibit in the Museum of Science, people are asked to choose between 50 or 100 random draws from a machine. The machine is known to have 60 green balls and 40 red balls. After each draw, the color of the ball is noted and the ball is put back fo
> A car manufacturer is concerned about poor customer satisfaction at one of its dealerships. The management decides to evaluate the satisfaction surveys of its next 40 customers. The dealer will be fined if the number of customers who report favorably is
> Consider a population proportion p = 0.12. a. Discuss the sampling distribution of the sample proportion with n = 20 and n = 50. b. Can you use the normal approximation to calculate the probability that the sample proportion is between 0.10 and 0.12 for
> Consider a population proportion p = 0.68. a. Calculate the expected value and the standard error of with n = 20. Is it appropriate to use the normal distribution approximation for? Explain. b. Calculate the expected value and the standard error of with
> A marketing firm opens a small booth at a local mall over the weekend, where shoppers are asked how much money they spent at the food court. The objective is to determine the average monthly expenditure of shoppers at the food court. Has the marketing fi
> We use the t distribution to construct a confidence interval for the population mean when the underlying population standard deviation is not known. Under the assumption that the population is normally distributed, find tα⁄2, df for the following scenari
> A small hair salon in Denver, Colorado, averages about 30 customers on weekdays with a standard deviation of 6. It is safe to assume that the underlying distribution is normal. In an attempt to increase the number of weekday customers, the manager offers
> The weight of people in a small town in Missouri is known to be normally distributed with a mean of 180 pounds and a standard deviation of 28 pounds. On a raft that takes people across the river, a sign states, “Maximum capacity 3,200 pounds or 16 person
> In 2010, Apple introduced the iPad, a tablet-style computer that its former CEO Steve Jobs called a “a truly magical and revolutionary product” (CNN, January 28, 2010). Suppose you are put in charge of determining the age profile of people who purchased
> In 2015, the U.S. Census Bureau reported that the median income for American households was $52,353, whereas the mean income was $71,932 (www.census.gov, data retrieved March 26, 2017). Suppose income can be represented by a lognormal variable, Y = eX, w
> A large technology firm receives an average of 12 new job applications every 10 days for positions that are not even advertised. Suppose the number of job applications received follows a Poisson distribution. a. What is the average number of days between
> The mileage (in 1,000s of miles) that car owners get with a certain kind of radial tire is a random variable having an exponential distribution with a mean of 50. a. What is the probability that a tire will last at most 40,000 miles? b. What is the proba
> The arrival time of an elevator in a 12-story dormitory is equally likely at any time range during the next 4 minutes. a. Calculate the expected arrival time. b. What is the probability that an elevator arrives in less than 1½ minutes? c. What is the pro
> According to the Federal Bureau of Investigation, there is a violent crime in the United States every 22 seconds (ABC News, September 25, 2007). Assume that the time between successive violent crimes is exponentially distributed. a. What is the probabili
> Suppose that the annual household income in a small Midwestern community is normally distributed with a mean of $55,000 and a standard deviation of $4,500. a. What is the probability that a randomly selected household will have an income between $50,000
> A new water filtration system is sold with a 10-year warranty that includes all parts and repairs. Suppose the life of this water filtration system is normally distributed with mean and standard deviation of 16 and 5 years, respectively. a. What is the p
> Five years after graduating from college, Lucia Li feels that she is finally ready to invest some of her earnings. She has eliminated her credit card debt and has established an emergency fund. Her parents have been pleased with the performance of their
> Suppose the average price of electricity for a New England customer follows the continuous uniform distribution with a lower bound of 12 cents per kilowatt-hour and an upper bound of 20 cents per kilowatt-hour. a. Calculate the average price of electrici
> Lisa Mendes and Brad Lee work in the sales department of an AT&T Wireless store. Lisa has been signing up an average of 48 new cell phone customers every month with a standard deviation of 22, while Brad signs up an average of 56 new customers with a sta
> U.S. consumers are increasingly viewing debit cards as a convenient substitute for cash and checks. The average amount spent annually on a debit card is $7,790 (Kiplinger’s, August 2007). Assume that the average amount spent on a debit card is normally d
> A florist makes deliveries between 1:00 pm and 5:00 pm daily. Assume delivery times follow the continuous uniform distribution. a. Calculate the mean and the variance of this distribution. b. Determine the percentage of deliveries that are made after 4:0
> On average, the state police catch eight speeders per hour at a certain location on Interstate 90. Assume that the number of speeders per hour follows the Poisson distribution. a. What is the probability that the state police wait less than 10 minutes f
> When crossing the Golden Gate Bridge traveling into San Francisco, all drivers must pay a toll. Suppose the amount of time (in minutes) drivers wait in line to pay the toll follows an exponential distribution with a probability density function of f (x)
> Customers make purchases at a convenience store, on average, every six minutes. It is fair to assume that the time between customer purchases is exponentially distributed. Jack operates the cash register at this store. a. What is the rate parameter λ? Wh
> According to the Daily Mail (February 28, 2012), there was an average of one complaint every 12 seconds against Britain’s biggest banks in 2011. It is reasonable to assume that the time between complaints is exponentially distributed. a. What is the mean
> Studies have shown that bats can consume an average of 10 mosquitoes per minute (berkshiremuseum.org). Assume that the number of mosquitoes consumed per minute follows a Poison distribution. a. What is the mean time between eating mosquitoes? b. Find the
> Let X be exponentially distributed with μ = 1.25. Compute the following values. a. P (X < 2.3) b. P (1.5 ≤ X ≤ 5.5) c. P (X > 7)
> Case Study 3.4 Nike’s Online Annual Report provides total revenues (in millions of $) for the Western Europe and Greater China regions for the years 2011 through 2015 as follows: (a). Nike Revenues in Western Europe and Greater China (i
> Let X be exponentially distributed with λ = 0.5. Compute the following values. a. P (X ≤ 1) b. P (2 < X < 4) c. P (X > 10)
> A random variable X is exponentially distributed with an expected value of 25. a. What is the rate parameter λ? What is the standard deviation of X? b. Compute P (20 ≤ X ≤ 30). c. Compute P (15 ≤ X ≤ 35).
> A random variable X is exponentially distributed with a mean of 0.1. a. What is the rate parameter λ? What is the standard deviation of X? b. Compute P (X > 0.20). c. Compute P (0.10 ≤ X ≤ 0.20).
> While Massachusetts is no California when it comes to sun, the solar energy industry is flourishing in this state (The Boston Globe, May 27, 2012). The state’s capital, Boston, averages 211.7 sunny days per year. Assume that the number of sunny days foll
> First introduced in Los Angeles, the concept of Korean-style tacos sold from a catering truck has been gaining popularity nationally (The New York Times, July 27, 2010). This taco is an interesting mix of corn tortillas with Korean-style beef, garnished
> A young investment manager tells his client that the probability of making a positive return with his suggested portfolio is 90%. If it is known that returns are normally distributed with a mean of 5.6%, what is the risk, measured by standard deviation,
> Scores on a marketing exam are known to be normally distributed with a mean and a standard deviation of 60 and 20, respectively. a. Find the probability that a randomly selected student scores between 50 and 80. b. Find the probability that a randomly se
> An estimated 1.8 million students take on student loans to pay ever-rising tuition and room and board (The New York Times, April 17, 2009). It is also known that the average cumulative debt of recent college graduates is about $22,500. Let the cumulative
> The manager of a night club in Boston stated that 95% of the customers are between the ages of 22 and 28 years. If the age of customers is normally distributed with a mean of 25 years, calculate its standard deviation.
> Due to a crisis in subprime lending, obtaining a mortgage has become difficult even for people with solid credit. In a report by the Associated Press (August 25, 2007), sales of existing homes fell for a 5th consecutive month, while home prices dropped f
> A packaging system fills boxes to an average weight of 18 ounces with a standard deviation of 0.2 ounce. It is reasonable to assume that the weights are normally distributed. Calculate the 1st, 2nd, and 3rd quartiles of the box weight.
> A financial advisor informs a client that the expected return on a portfolio is 8% with a standard deviation of 12%. There is a 15% chance that the return would be above 16%. If the advisor is right about her assessment, is it reasonable to assume that t
> For a continuous random variable X, P (20 ≤ X ≤ 40) = 0.15 and P (X > 40) = 0.16. Calculate the following probabilities. a. P (X < 40) b. P (X < 20) c. P (X = 40)
> Let X be normally distributed with μ = −15 and σ = 9. a. Find P (X > −12). b. Find P (0 ≤ X ≤ 5). c. Find x such that P (X ≤ x) = 0.25. d. Find x such that P (X > x) = 0.25.
> Let X be normally distributed with μ = 254 and σ = 11. a. Find P (X ≤ 266). b. Find P (250 < X < 270). c. Find x such that P (X ≤ x) = 0.33. d. Find x such that P (X > x) = 0.33.
> The random variable X is normally distributed. Also, it is known that P (X > 150) = 0.10. a. Find the population mean μ if the population standard deviation σ = 15. b. Find the population mean μ if the population standard deviation σ = 25. c. Find the po
> Let X be normally distributed with mean μ = 2,500 and standard deviation σ = 800. a. Find x such that P (X ≤ x) = 0.9382. b. Find x such that P (X > x) = 0.025. c. Find x such that P (2500 ≤ X ≤ x) = 0.1217. d. Find x such that P (X ≤ x) = 0.4840.
> Find the following z values for the standard normal variable Z. a. P (Z ≤ z) = 0.1020 b. P (z ≤ Z ≤ 0) = 0.1772 c. P (Z > z) = 0.9929 d. P (0.40 ≤ Z ≤ z) = 0.3368
> Find the following z values for the standard normal variable Z. a. P (Z ≤ z) = 0.9744 b. P (Z > z) = 0.8389 c. P (−z ≤ Z ≤ z) = 0.95 d. P (0 ≤ Z ≤ z) = 0.3315
> Find the following probabilities based on the standard normal variable Z. a. P(−0.67 ≤ Z ≤ −0.23) b. P (0 ≤ Z ≤ 1.96) c. P (−1.28 ≤ Z ≤ 0) d. P (Z > 4.2)
> A study reports that recent college graduates from New Hampshire face the highest average debt of $31,048 (The Boston Globe, May 27, 2012). A researcher from Connecticut wants to determine how recent undergraduates from that state fare. He collects data
> Find the following probabilities based on the standard normal variable Z. a. P (Z > 0.74) b. P (Z ≤ −1.92) c. P (0 ≤ Z ≤ 1.62) d. P (−0.90 ≤ Z ≤ 2.94)
> Find the following probabilities based on the standard normal variable Z. a. P (Z > 1.32) b. P (Z ≤ −1.32) c. P (1.32 ≤ Z ≤ 2.37) d. P (−1.32 ≤ Z ≤ 2.37)
> You have been informed that the assessor will visit your home sometime between 10:00 am and 12:00 pm. It is reasonable to assume that his visitation time is uniformly distributed over the specified two-hour interval. Suppose you have to run a quick erran
> The scheduled arrival time for a daily flight from Boston to New York is 9:25 am. Historical data show that the arrival time follows the continuous uniform distribution with an early arrival time of 9:15 am and a late arrival time of 9:55 am. a. Calculat
> Forty-four percent of consumers with credit cards carry balances from month to month (bankrate.com, February 20, 2007). Four consumers with credit cards are randomly selected. a. What is the probability that all four consumers carry a credit card balance
> Fifty percent of the customers who go to Sears Auto Center for tires buy four tires and 30% buy two tires. Moreover, 18% buy fewer than two tires, with 5% buying none. a. Find the expected value and the standard deviation of the number of tires a custome
> Assume that X is a hypergeometric random variable with N = 25, S = 3, and n = 4. Calculate the following probabilities. a. P (X = 0) b. P (X = 1) c. P (X ≤ 1)
> Airline travelers should be ready to be more flexible as airlines once again cancel thousands of flights this summer. The Coalition for Airline Passengers Rights, Health, and Safety averages 400 calls a day to help stranded travelers deal with airlines (
> Motorists arrive at a Gulf gas station at the rate of two per minute during morning hours. a. What is the probability that more than two motorists will arrive at the Gulf gas station during a one-minute interval in the morning? b. What is the probability
> A textile manufacturing process finds that on average, two flaws occur per every 50 yards of material produced. a. What is the probability of exactly two flaws in a 50-yard piece of material? b. What is the probability of no more than two flaws in a 50-y
> An article in the National Geographic News (“U.S. Racking Up Huge Sleep Debt,” February 24, 2005) argues that Americans are increasingly skimping on their sleep. A researcher in a small Midwestern town wants to estimate the mean weekday sleep time of its
> A tollbooth operator has observed that cars arrive randomly at an average rate of 360 cars per hour. a. Find the probability that two cars arrive during a specified one-minute period. b. Find the probability that at least two cars arrive during a specifi
> Let the mean success rate of a Poisson process be 8 successes per hour. a. Find the expected number of successes in a half-hour period. b. Find the probability of at least two successes in a given half-hour period. c. Find the expected number of successe
> Assume that X is a Poisson random variable with μ = 4. Calculate the following probabilities. a. P (X = 4) b. P (X = 2) c. P (X ≤ 1)
> Assume that X is a Poisson random variable with μ = 1.5. Calculate the following probabilities. a. P (X = 1) b. P (X = 2) c. P (X ≥ 2)
> The Washington, DC, region has one of the fastest-growing foreclosure rates in the nation, as 15,613 homes went into foreclosure during the one-year period ending in February 2008 (The Washington Post, June 19, 2008). Over the past year, the number of fo
> The principal of an architecture firm tells her client that there is at least a 50% chance of having an acceptable design by the end of the week. She knows that there is only a 25% chance that any one designer would be able to do so by the end of the wee
> Sixty percent of a firm’s employees are men. Suppose four of the firm’s employees are randomly selected. a. What is more likely, finding three men and one woman or two men and two women? b. Do you obtain the same answer as in part a if 70% of the firm’s
> According to the U.S. Census, roughly half of all marriages in the United States end in divorce. Researchers from leading universities have shown that the emotions aroused by one person’s divorce can transfer like a virus, making divorce contagious (CNN,
> Sikhism, a religion founded in the 15th century in India, is going through turmoil due to a rapid decline in the number of Sikh youths who wear turbans (The Washington Post, March 29, 2009). The tedious task of combing and tying up long hair and a desire
> In an analysis of Census figures, one in four American counties has passed or is approaching the tipping point where black, Hispanic, and Asian children constitute a majority of the under-20 population (The New York Times, August 6, 2008). Racial and eth
> In order to estimate the mean 30-year fixed mortgage rate for a home loan in the United States, a random sample of 28 recent loans is taken. The average calculated from this sample is 5.25%. It can be assumed that 30-year fixed mortgage rates are normall
> Approximately 45% of Baby Boomers—those born between 1946 and 1964—are still in the workforce (www.pewresearch.org, May 11, 2015). Six Baby Boomers are selected at random. a. What is the probability that exactly one of the Baby Boomers is still in the wo
> According to a survey by Transamerica Center for Health Studies, 15% of Americans still have no health insurance even after passage of the Affordable Care Act, better known as Obamacare (www.cbsnews.com, September 24, 2014). Suppose five individuals are
> Let the probability of success on a Bernoulli trial be 0.30. In five Bernoulli trials, what is the probability that there will be (a) four failures, and (b) more than the expected number of failures?
> Assume that X is a binomial random variable with n = 8 and p = 0.32. Calculate the following probabilities. a. P (3 < X < 5) b. P (3 < X ≤ 5) c. P (3 ≤ X ≤ 5)
> Megan Hanson, a realtor in Brownsburg, Indiana, would like to use estimates from a multiple regression model to help prospective sellers determine a reasonable asking price for their homes. She believes that the following four factors influence the askin
> Akiko Hamaguchi, the manager at a small sushi restaurant in Phoenix, Arizona, is concerned that the weak economic environment has hampered foot traffic in her area, thus causing a dramatic decline in sales. Her cousin in San Francisco, Hiroshi Sato, owns
> A local university offers its employees the following Fidelity investment products for their retirement plans: Fidelity Total Bond Fund Fidelity Short-Term Bond Fund Fidelity Magellan Fund Fidelity International Small Cap Fund Fidelity Freedom Income
> Executive compensation has risen dramatically beyond the rising levels of an average worker’s wage over the years. The government is even considering a cap on high-flying salaries for executives (The New York Times, February 9, 2009). C
> Assume that X is a binomial random variable with n = 6 and p = 0.68. Calculate the following probabilities. a. P (X = 5) b. P (X = 4) c. P (X ≥ 4)
> In a multiple regression with four explanatory variables and 100 observations, it is found that SSR = 4.75 and SST = 7.62. a. Calculate the standard error of the estimate se. b. Calculate the coefficient of determination R2. c. Calculate adjusted R2.
> A financial analyst uses the following model to estimate a firm’s stock return: Return = β0 + β1P⁄E + β2P/S + ε, where P/E is a firm’s price-to-earnings ratio and P/S is a firm’s price-to sales ratio. For a sample of 30 firms, she finds that SSE = 4,402.
> For a sample of 41 New England cities, a sociologist studies the crime rate in each city (crimes per 100,000 residents) as a function of its poverty rate (in %) and its median income (in $1,000s). He finds that SSE = 4,182,663 and SST = 7,732,451. a. Ca
> In a multiple regression with two explanatory variables, and 50 observations, it is found that SSE = 35 and SST = 90. a. Calculate the standard error of the estimate se. b. Calculate the coefficient of determination R2.
