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business statistics communicating

Business Statistics Communicating With Numbers 1st Edition Kelly Jaggia - Solutions

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) 4 failures, (b) more than the expected number of failures? L05
Assume th a t X is a binomial random variable with n = 8 and p = 0.32. Calculate the following probabilities. L05a. P(3 < X < 5)b. P(3 < X ≤ 5)c. P(3 ≤ X ≤ 5)
Assume th a t X is a binomial random variable with n = 6 and p = 0.68. Calculate the following probabilities. L05a. P(X = 5)b. P(X = 4)c. P( X ≥ 4)
Assume that X is a binomial random variable with n = 5 and p = 0.35. Calculate the following probabilities. L05a. P(X = 0)b. P(X = 1)c. P(X ≤ 1)
You own a portfolio that has $4,400 invested in stocks and$5,600 invested in bonds. W hat is the expected return o f the portfolio if stocks and bonds are expected to yield a return of 9% and 5%, respectively? L05
What are the portfolio weights for a portfolio that has 100 shares o f Stock X that sell for $20 per share and 200 shares of Stock Y that sell for $12 per share? L05
Market observers are quite uncertain whether the stock market has bottomed out from the economic meltdown that began in 2008. In an interview on March 8,2009, CNBC interviewed two prominent economists who offered differing views on whether the U.S. economy was getting stronger or weaker. An
You are considering buying insurance for your new laptop computer, which you have recently bought for $1,500. The insurance premium for three years is $80. Over the threeyear period there is an 8% chance that your laptop com puter w ill require w ork w o rth $400, a 3% chance that it w ill require
Organizers of an outdoor summer concert in Toronto are concerned about the weather conditions on the day of the concert. They w ill make a profit o f $25,000 on a clear day and$10,000 on a cloudy day. They will make a loss of $5,000 if it rains. The weather channel has predicted a 60% chance of
In early 2010, lead ing U.S. stock m arkets tu m b le d m ore tha n 2.5% as U.S. consumer confidence fell to its lowest level since August 2009 (BBC News, July 16, 2010). Given fresh economic data, an economist believes there is a 35% chance that consumer confidence will fall below 62 and only a
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 th a t he w ill m ake o n e o f th e shots, and a 20% chance that he will make both shots.a. Construct
Graphically depict the probability distribution and comment on its symmetry/skewness. L05
W hat is the probability that a reader carries at least two credit cards? L05
W hat is the probability that a reader carries less than two credit cards? L05
W hat is the probability that a reader carries no credit cards? L05
Is this a valid probability distribution? L05
Describe the hypergeometric distribution and compute relevant probabilities. L05
Describe the Poisson distribution and compute relevant probabilities. L05
Describe the binomial distribution and compute relevant probabilities. L05
Compute summary measures to evaluate portfolio returns. L05
Differentiate among risk neutral, risk averse, and risk loving consumers. L05
Calculate and interpret summary measures for a discrete random variable. L05
Describe the probability distribution of a discrete random variable. L05
Distinguish between discrete and continuous random variables. L05
The chefs at a local pizza chain in Cambria, California, strive to maintain the suggested size of their 16-inch pizzas. Despite their best efforts, they are unable to make every pizza exactly 16 inches in diameter. The manager has determined that the size of the pizzas is normally distributed with
Consider the information presented in the introductory case of this chapter. Recall that Anne wants to determine if the marketing campaign has had a lingering effect on the amount of money customers spend on iced coffee. Before the campaign, customers spent an average of $4.18 on iced coffee with a
Many people apply for jobs to serve as paramedics or firefighters, yet they cannot complete basic physical fitness standards. A recent study found that 77% of all candidates for paramedic and firefighter positions were overweight or obese (Obesity, March 19, 2009).a. What is the expected value and
Consider the information presented in the introductory case of this chapter. Recall that Anne Jones wants to determine if the marketing campaign has had a lingering effect on the proportion of customers who are women and teenage girls. Prior to the campaign, 43% of the customers were women and 21%
A large introductory marketing class has 340 students. The class is divided up into 10 groups for the final course project. Connie is in a group of 34 students. These students had averaged 72 on the midterm, when the class as a whole had an average score of 73 with a standard deviation of 10.
The home ownership rate during 2009 declined to approximately 67% and is now comparable to the rate in early 2000 ( U.S. Census Bureau News, February 2, 2010).A random sample of 80 households is taken from a small island community with 1,000 households. The home ownership rate on the island is
A firm that produces one-gallon jugs of milk wants to ensure that the machine is operating properly. Every two hours, the company samples 25 jugs and calculates the following sample mean filling weights (in ounces):128.7 128.4 128.0 127.8 127.5 126.9 Assume that when the machine is operating
In a 2010 automotive quality study conducted by J.D. Power & Associates, Toyota Motor Corp. was rated below average, falling to 21st place from 7th the year before (The Wall Street Journal, June 18, 2010). Toyota’s reputation suffered due to massive recalls in late 2009 and early 2010 related to
A simple random sample is a sample of n observations which has the same probability of being selected from the population as any other sample of n observations. Most statistical methods presume simple random samples. L056
A sampling bias occurs when the information from a sample is not typical of that in the population in a systematic way. Selection bias refers to a systematic exclusion of certain groups from consideration for the sample. Nonresponse bias refers to a systematic difference in preferences between
The numerical measure of a population is called a population parameter, or simply a parameter. A parameter is a constant even though its value may be unknown. The numerical measure of a sample is called a sample statistic, or simply a statistic. A statistic, such as the sample mean or the sample
Report the probabilities that at least 200 college graduates and at least 100 high school graduates under age 25 are employed. L056
Compute the expected number of college and high school graduates who are employed. L056
The producer of a particular brand of soup claims that its sodium content is 50% less than that of its competitor.The food label states that the sodium content measures 410 milligrams per serving. Assume the population of sodium content is normally distributed with a standard deviation of 25
Presidential job approval is the most-watched statistic in American politics. According to the June 2010 NBC/wall Street Journal public opinion poll, President Barack Obama has reached his lowest approval rating since taking office in January of 2009. The poll showed that 48% of people disapprove
American workers are increasingly planning to delay retirement (US 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.a. What is the probability that in a sample of
According to a recent report, scientists in New England say they have identified a set of genetic variants that predicts extreme longevity with 77% accuracy (New York Times, July 1, 2010). Assume 150 patients decide to get their genome sequenced.a. If the claim by scientists is accurate, what is
Data from the Bureau of Labor Statistics'Consumer Expenditure Survey (CE) show that annual expenditures for cellular phone services per consumer unit increased from $210 in 2001 to $608 in 2007. Let the standard deviation of annual cellular expenditure be $48 in 2001 and $132 in 2007.a. What is the
The average college graduate has a student loan debt of $23,186 (The Boston Globe, June 8 , 2010). Assume the population standard deviation is $5,000. Suppose you take a random sample of 50 college graduates.a. What is the probability that the sample mean debt is more than $25,000?b. What is the
Trader Joe's is a privately held chain of specialty grocery stores in the U.S. Starting out as a small chain of convenience stores, it has expanded to over 340 stores as of June 2010 (Traderjoe.com). It has developed a reputation as a unique grocery store selling products such as gourmet foods,
An automatic machine in a manufacturing process is operating properly if the length of an important subcomponent is normally distributed with a mean μ = 80 cm and standard deviation σ = 2 cm.a. Find the probability that the length of one randomly selected unit is less than 79 cm.b. Find the
While starting salaries have fallen for college graduates in many of the top hiring fields, there is some good news for business undergraduates with concentrations in accounting and finance (Bloomberg Businessweek, July 1, 2010). According to the National Association of Colleges and
According to the Bureau of Labor Statistics it takes an average of 22 weeks for someone over 55 to find a new job, compared with 16 weeks for younger workers (The Wall Street Journal, September 2 , 2008). Assume that the probability distributions are normal and that the standard deviation is 2
In the previous question regarding walking regimens o f the residents of Miami, explain how you can obtain a representative sample based on the following sampling strategies:a. Simple random sampling.b. Stratified random sampling.c. Cluster sampling. L056
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 working for a public health institute based in
The college admissions office at a local university usually admits 750 students and knows from previous experience that 25% of these students choose not to enroll at the university. Assume p = 0.25.a. Construct the centerline and the upper and lower control limits for the chart.b. Assume that this
A manufacturing process produces steel rods in batches of 1,000. The firm believes that the percent of defective items generated by this process is 5%.a. Construct the centerline and the upper and lower control limits for the chart.b. An engineer inspects the next batch of 1,000 steel rods and
A random sample of size n = 500 is taken from a population with p = 0.34.a. Construct the centerline and the upper and lower control limits for the chart.b. Suppose six m ore sam ples of size 500 w ere drawn, producing th e following sam ple proportions: 0.2 8 , 0.30, 0 .3 3 , 0 .3 4 , 0.37, and
A random sample of size n = 400 is taken from a population with p = 0.10.a. Construct the centerline and the upper and lower control limits for the chart.b. Suppose six more samples of size 400 were drawn, producing the following sample proportions: 0.06, 0.11, 0 .0 9 , 0 .0 8 , 0.14, and 0.16.
A random sample is taken from a population with p = 0.04.a. Construct the centerline and the upper and lower control limits for th e chart if a random sam ple of size n = 250 is used.b. Repeat the analysis with n = 150.c. Discuss the effect of the sample size on the control limits. L056
A random sample of size n = 36 is 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 m ore sam ples of size 36 w ere drawn, producing th e following sam ple m eans: 1 3 3 , 1 4 2
A random sample of size n = 25 is taken from a 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 more samples of size 25 were drawn producing the following sample means: 18, 16, 19, 24, 28, and
Consider a 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. Discuss the effect of the sample size on the control limits. L056
Despite the recession, com panies are setting aside a large chunk of their IT spending for green technology projects (BusinessWeek, March 5 , 2009). Two out of three of the large companies surveyed by Deloitte said they have at least 5% of their IT budget earmarked for green IT projects. Suppose th
Given the recent economic downturn, only 60% in a graduating class of 250 will find em ploym ent in the first round of a job search. You have 20 friends w ho have recently graduated.a. Discuss th e sam pling distribution of th e sam ple proportion of your friends w ho will find em ploym ent in th e
Suppose in the previous question th e analyst had random ly chosen 12 CEO com pensations for 2006.a. Is it necessary to apply th e finite population correction factor? Explain.b. Is th e sam pling distribution of th e sam ple m ean normally distributed? Explain.c. Calculate th e expected value and
The issues surrounding th e levels and structure of executive com pensation have gained added prom inence in th e wake of th e financial crisis th a t erupted in th e fall of 2008. Based on the 2006 com pensation data obtained from the Securities and Exchange C om m ittee (SEC) website, it was
A random sam ple of size n = 80 is taken from a population of size N = 600 with a population proportion p = 0.46.a. Is it necessary to apply th e finite population correction factor? Explain. Calculate th e expected value and the standard deviation of th e sam ple proportion.b. W hat is th e
A random sam ple of size n = 100 is taken from a population of size N = 3,000 with a population proportion of p = 0.34.a. Is it necessary to apply th e finite population correction factor? Explain. Calculate th e expected value and the standard deviation of th e sam ple proportion.b. W hat is th e
A random sam ple of size n = 70 is taken from a finite population of size N = 500 with m ean μ = 220 and variance σ 2 = 324.a. Is it necessary to apply th e finite population correction factor? Explain. Calculate th e expected value and the standard deviation of th e sam ple m ean.b. W hat is th
A random sam ple of size n = 100 is taken from a population of size N = 2,500 with m ean μ = —45 and variance σ2 = 81.a. Is it necessary to apply th e finite population correction factor? Explain. Calculate the expected value and the standard deviation of th e sam ple m ean.b. W hat is th e
After years of rapid growth, illegal immigration into the United States has declined, perhaps owing to the recession and increased border enforcement by the U.S. (Los Angeles Times, September 1, 2010). While its share has declined, California still accounts for 23% of the nation's estimated 11.1
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 for the next draw. You win a prize if more than
Europeans are increasingly upset at their leaders for making deep budget cuts to many social programs that are becoming too expensive to sustain. For instance, the popularity of President Nicolas Sarkozy of France has plummeted, giving him an approval rating of just 26% (The Wall Street Journal,
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 fewer than 26 customers report favorably and the dealership will be dissolved if fewer than
According to a recent FCC survey, one in six cell phone users have experienced "bill shock" from unexpectedly high cell phone bills (Tech Daily Dose, May 26, 2010).a. Discuss the sampling distribution of the sample proportion based on a sample of 200 cell phone users. Is it appropriate to use the
A recent study by Allstate Insurance Co. finds that 82% of teenagers have used cell phones while driving (The Wall Street Journal, May 5 , 2010). Suppose a random sample of 100 teen drivers is taken.a. Discuss the sampling distribution of the sample proportion.b. What is the probability that the
A random sample of size n = 200 is taken from a population with population proportion p = 0.75.a. Calculate the expected value and the standard deviation for the sampling distribution of the sample proportion.b. What is the probability that the sample proportion is between 0.70 and 0.80?c. What 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 both sample sizes?c. Report the probabilities
Consider a population proportion p = 0.68.a. Calculate the expected value and the standard deviation of with n = 20. Is it appropriate to use the normal distribution approxim ation for Explain.b. Calculate the expected value and th e standard deviation of with n = 50. Is it appropriate to use the
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 a $2 discount on 5 consecutive weekdays.She
The weight of turkeys is known to be normally distributed with a mean of 22 pounds and a standard deviation of 5 pounds.a. Discuss the sampling distribution of the sample mean based on a random draw of 16 turkeys.b. Find the probability that the mean weight of 16 randomly selected turkeys is more
The w eight o f people in a small town in Missouri is known to be normally distributed w ith a mean o f 180 pounds and a standard deviation of 28 pounds. On a raft that takes people across the river, a sign states, "Maxim um capacity 3,200 pounds or 16 persons." What is the probability that a
Despite its nutritional value, seafood is only a tiny part of the American diet, with the average American eating just 16 pounds of seafood per year. Janice and Nina both work in the seafood industry and they decide to create their own random samples and document the average seafood diet in their
Beer bottles are filled so that they contain 330 ml of beer in each bottle. Suppose that the amount of beer in a bottle is normally distributed with a standard deviation of 4 ml.a. What is the probability that a randomly selected bottle will have less than 325 ml of beer?b. What is the probability
According to a recent survey, high school girls average 100 text messages daily (The Boston Globe, April 21, 2010). Assume the population standard deviation is 20 text messages. Suppose a random sample of 50 high school girls is taken.a. What is the probability that the sample mean is more than
A random sample of size n = 50 is taken from a population with mean μ = -9 .5 and standard deviation σ = 2.a. Calculate the expected value and the standard deviation for the sampling distribution of the sample mean.b. What is the probability that the sample mean is less than — 10?c. What is the
A random sample of size n = 100 is taken from a population with mean μ = 80 and standard deviation σ = 14.a. Calculate the expected value and the standard deviation for the sampling distribution of the sample mean.b. What is the probability that the sample mean falls between 77 and 85?c. What is
A random sample is drawn from a population with meanμ = 66 and standard deviation σ = 5.5.a. Comment on the distribution of the sample mean with n = 16 and n = 36.b. Can you use the standard normal distribution to calculate the probability that the sample mean falls between 66 and 68 for both
A random sample is drawn from a normally distributed population with mean μ = 12 and standard deviation σ = 1.5.a. Comment on the sampling distribution of the sample mean with n = 20 and n = 40.b. Can you use the standard normal distribution to calculate the probability that the sample mean is
In the previous question regarding Vons' store hours, explain how you can obtain a representative sample based on the following sampling strategies:a. Simple random sampling.b. Stratified random sampling.c. Cluster sampling. L01
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 envelope to randomly selected residents in the Grover
Natalie Min is a business student 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
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 m onthly expenditure o f shoppers at the food court.Has the marketing firm com m itted any sampling bias? Discuss.
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 the iPad in the U.S. Explain in detail the
Construct and interpret control charts for quantitative and qualitative data. L01
Use a finite population correction factor. L01
Describe the properties of the sampling distribution of the sample proportion. L01
Explain the importance of the central limit theorem. L01
Describe the properties of the sampling distribution of the sample mean. L01
Distinguish between stratified random sampling and cluster sampling. L01
Describe simple random sampling. L01
Explain common sample biases. L01
Differentiate between a population parameter and a sample statistic. L01
A manager of a local drugstore is projecting next month’s sales for a particular cosmetic line. She knows from historical data that sales follow a continuous uniform distribution with a lower limit of $2,500 and an upper limit of $5,000.a. What are the mean and standard deviation of this uniform
An investment strategy has an expected return of 4% and a standard deviation of 6%. Assume that investment returns are normally distributed. Use the empirical rule to answer the following questions.a. What is the probability of earning a return greater than 10%?b. What is the probability of earning

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