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 the GPA of students with whom she might be competing. She randomly surveys 40 students from her accounting class for the analysis. Discuss in detail whether or not Natalie’s analysis is based on a representative sample.
> FILE Gas_Prices. The accompanying table shows a portion of the average price (in $) for a gallon of gas for the 50 states during April 2012. State …………………………………………………………………………………………………. Price Alabama ………………………………………………………………………………………………… 4.36 Alaska ………
> The accompanying table shows a portion of median house values (in $) for the 50 states as reported by the U.S. Census Bureau in 2010. State ………………………………………………………………………………………. House Value Alabama ………………………………………………………………………………………….. 117600 Alaska …………………
> A popular weight loss program claims that with its recommended healthy diet regimen, users lose significant weight within a month. In order to estimate the mean weight loss of all customers, a nutritionist takes a sample of 18 dieters and records their w
> The following table lists a portion of the average math SAT scores for each state for the year 2009. State …………………………………………………………………………………………. SAT Alabama ……………………………………………………………………………………… 552 Alaska …………………………………………………………………………………………. 516 ⋮ ……………………………
> The following ogive summarizes the salary (in $1,000,000s) for the 30 highest-paid players in the National Basketball Association (NBA) for the 2012 season (www.nba.com, data retrieved March 2012). a. Approximate the percentage of salaries that were le
> Consider the following five-point summary that was obtained from a data set with 200 observations. a. Interpret Q1 and Q3. b. Calculate the interquartile range. Determine whether any outliers exist. c. Is the distribution symmetric? If not, comment o
> Calculate the 20th, 40th, and 70th percentiles for the following data set -300 -257 -325 -234 -297 -362 -255
> The following ogive summarizes the median household income for the 50 states in the United States (U.S. Census, 2010). a. Approximate the percentage of states with median household income less than $50,000. b. Approximate the percentage of states with
> Calculate the 20th, 50th, and 80th percentiles for the following data set 120 215 187 343 268 196 312
> The manager of a nightclub near a local university recorded the ages of the last 100 guests in the following cumulative frequency distribution. Ages ……………………………………………………………………….. Cumulative Frequency 18 up to 22 ……………………………………………………………………………………………. 45 2
> Fifty cities provided information on vacancy rates (in percent) in local apartments in the following frequency distribution Vacancy Rate (in percent) ……………………………………………………………… Frequency 0 up to 3 …………………………………………………………………………………………………… 5 3 up to 6 …………………
> The following relative frequency distribution summarizes the ages of women who had a child in the last year. Ages …………………………………………………………………………………. Relative Frequency 15 up to 20 ………………………………………………………………………………………………. 0.10 20 up to 25 ……………………………………………………
> AccuWeather.com listed the following high temperatures (in degrees Fahrenheit) for 33 European cities on July 21, 2010. a. Construct the frequency distribution using classes of 60 up to 70, 70 up to 80, etc. b. Construct the relative frequency, the cu
> FILE DOW Characteristics. The accompanying table shows a portion of the 30 companies that comprise the Dow Jones Industrial Average (DJIA). The second column shows the year that the company joined the DJIA (Year). The third column shows each company&acir
> The number of text messages sent by 25 13-year-olds over the past month are as follows a. Construct the frequency distribution using classes of 500 up to 600, 600 up to 700, etc. b. Construct the relative frequency distribution, the cumulative frequen
> Kiplinger’s (August 2007) lists the assets (in billions of $) for the 20 largest stock mutual funds (ranked by size) as follows: a. Construct the frequency distribution using classes of 40 up to 70, 70 up to 100, etc. b. Construct the
> Consider the following five-point summary that was obtained from a data set with 500 observations. a. Interpret Q1 and Q3. b. Calculate the interquartile range. Determine whether any outliers exist. c. Is the distribution symmetric? If not, comment o
> Consider the following relative frequency distribution: Class ……………………………………………………………………… Relative Frequency –20 up to –10 ……………………………………………………………………………….. 0.04 –10 up to 0 …………………………………………………………………………………. 0.28 0 up to 10 …………………………………………………………………………………
> Consider the following frequency distribution: Class ……………………………………………………………………………………. Frequencyy 1,000 up to 1,100 ………………………………………………………………………………… 2 1,100 up to 1,200 ………………………………………………………………………………… 7 1,200 up to 1,300 ………………………………………………………………………………… 3
> Consider the following frequency distribution: Class ………………………………………………………………………………… Frequency 10 up to 20 ……………………………………………………………………………………. 12 20 up to 30 ……………………………………………………………………………………. 15 30 up to 40 ……………………………………………………………………………………. 25 40 up to 50
> Consider the following data set: a. Construct the frequency distribution using classes of −10 up to 0, 0 up to 10, etc. How many of the observations are at least 10 but less than 20? b. Construct the relative frequency distribution an
> Calculate the mean, the variance, and the standard deviation of the following discrete probability distribution. / /
> Calculate the mean, the variance, and the standard deviation of the following discrete probability distribution. 10 15 20 P (X = x) 0.35 0.30 0.20 0.15
> Vanguard’s Precious Metals and Mining fund (Metals) and Fidelity’s Strategic Income fund (Income) were two top-performing mutual funds for the years 2000 through 2009. An analysis of annual return data for these two funds provided important information f
> When reviewing the overall strength of a particular firm, financial analysts typically examine the net profit margin. This statistic is generally calculated as the ratio of a firm’s net profit after taxes (net income) to its revenue, expressed as a perce
> A recent survey of 992 people asked: In which professional sport—football, boxing, hockey, or martial arts—is an athlete most likely to sustain an injury that will affect the athlete after he or she retires? (Vanity Fa
> The following table shows Fortune 500’s rankings of America’s 10 largest corporations for 2010. Next to each corporation is its market capitalization (in $ billions as of March 26, 2010) and its total return (in %) to
> Professor Sanchez has been teaching Principles of Economics for over 25 years. He uses the following scale for grading. a. Depict the above probability distribution graphically. Comment on whether or not the probability distribution is symmetric. b. Co
> A 2010 poll conducted by NBC asked respondents who would win Super Bowl XLV in 2011. The responses by 20,825 people are summarized in the following table. Atlanta Falcons …………………………………………………………………………….… 4,040 New Orleans Saints …………………………………………………………………
> A basketball player is fouled while attempting to make a basket and receives two free throws. The opposing coach believes there is a 55% chance that the player will miss both shots, a 25% chance that he will make one of the shots, and a 20% chance that h
> A financial analyst creates the following probability distribution for the performance of an equity income mutual fund. a. Comment on the optimism or pessimism depicted in the analyst’s estimates. b. Convert the above probability dist
> India is the second most populous country in the world, with a population of over 1 billion people. Although the government has offered various incentives for population control, some argue that the birth rate, especially in rural India, is still too hig
> Identify the possible values of the following random variables. Which of the random variables are discrete? a. The advertised size of a round Domino’s pizza. b. The actual size of a round Domino’s pizza. c. The number of daily visitors to Yosemite Nation
> A random sample is drawn from a population with mean μ = 66 and standard deviation σ = 5.5. a. Comment on the sampling distribution of the sample mean with n = 16 and n = 36. b. Can you use the standard normal distribution to calculate the probability th
> In the previous question, suppose that the management decides to use a chart for the analysis. As noted earlier, 10% of produced items are known to be nonconforming. The firm analyzes a batch of production items for 6 weeks and computes the following per
> 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
> 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
> 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 deviatio
> 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
