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Business Statistics 3rd Edition Norean Sharpe, Richard Veaux, Paul Velleman - Solutions

A marketing agency has developed three vacation packages to promote a timeshare plan at a new resort. They estimate that 20% of potential customers will choose the Day Plan, which does not include overnight accommodations; 40% will choose the Overnight Plan, which includes one night at the resort;
Given independent random variables, X and Y, with means and standard deviations as shown, find the mean and standard deviation of each of the variables in parts a to d.a) 3Xb) Y + 6c) X+ Yd) X-Y
Suppose occurrences of sales on a small company’s website are well modeled by a Poisson model with A — 5/hour. a) If a sale just occurred, what it the expected waiting time until the next sale? b) What is the probability that the next sale will happen in the next 6 minutes?
In the first quarter of 2013, a group of domestic equity mutual funds had a mean return of 6.2% with a standard deviation of 1.8%. If a Normal model can be used to model them, what percent of the funds would you expect to be in each region? Be sure to draw a picture first. a) Returns of 8.0% or
Although controversial and the subject of some recent law suits (e.g., Satchell et al. vs. FedEx Express), some human resource departments administer standard IQ tests to all employees. The Stanford-Binet test scores are well modeled by a Normal model with mean 100 and standard deviation 16. If the
From the mutual funds in Exercise 23 with quarterly returns that are well modeled by a Normal model with a mean of 6.2% and a standard deviation of 1.8%, find the cutoff return value(s) that would separate the a) Highest 50%. b) Highest 16%. c) Lowest 2.5%. d) Middle 68%.
For the IQ test administered by human resources and discussed in Exercise 24, what cutoff value would separate the a) Lowest 0.15% of all applicants? b) Lowest 16%? c) Middle 95%? d) Highest 2.5%?
The daily exchange rates for the five-year period 2008 to 2013 between the euro (EUR) and the British pound (GBP) can be modeled by a Normal distribution with mean 1.19 euros (to pounds) and standard deviation 0.043 euros. Given this model, what is the probability that on a randomly selected day
For the 300 trading days from January 11, 2012 to March 22, 2013, the daily closing price of IBM stock (in $) is well modeled by a Normal model with mean $197.92 and standard deviation $7.16. According to this model, what is the probability that on a randomly selected day in this period the stock
For the model of the EUR/GBP exchange rate discussed in Exercise 27, what would the cutoff rates be that would separate the a) Highest 16% of EUR/GBP rates? b) Lowest 50%? c) Middle 95%? d) Lowest 2.5%?
According to the model in Exercise 28, what cutoff value of price would separate the a) Lowest 16% of the days? b) Highest 0.15%? c) Middle 68%? d) Highest 50%?
According to the Normal model N(0.062, 0.018) describing mutual fund returns in the 1st quarter of 2013 in Exercise 23, what percent of this group of funds would you expect to have return a) Over 6.8%? b) Between 0% and 7.6%? c) More than 1 %? d) Less than 0%?
Based on the Normal model N (100, 16) describing IQ scores from Exercise 24, what percent of applicants would you expect to have scores? a) Over 80? b) Under 90? c) Between 112 and 132? d) Over 125?
Based on the model Af(0.062, 0.018) for quarterly returns from Exercise 23, what are the cut-off values for the a) Highest 10% of these funds? b) Lowest 20%? c) Middle 40%? d) Highest 80%?
In the Normal model N(100, 16) for IQ scores from Exercise 24, what cutoff value bounds the a) Highest 5% of all IQs? b) Lowest 30% of the IQs? c) Middle 80% of the IQs? d) Lowest 90% of all IQs?
Consider the Normal model N(0.062, 0.018) for returns of mutual funds in Exercise 23 one last time. a) What value represents the 40th percentile of these returns? b) What value represents the 99th percentile? c) What’s the IQR of the quarterly returns for this group of funds?
Consider the IQ model N(100, 16) one last time. a) What IQ represents the 15th percentile? b) What IQ represents the 98th percentile? c) What’s the IQR of the IQs?
Every Normal model is defined by its parameters, the mean and the standard deviation. For each model described here, find the missing parameter. As always, start by drawing a picture. a) μ = 20, 45% above 30; σ ? b) μ = 88, 2% below 50; σ ? c) σ = 5, 80% below 100; μ = ? d) σ = 15.6, 10%
Every Normal model is defined by its parameters, the mean and the standard deviation. For each model described here, find the missing parameter. Don’t forget to draw a picture. a) μ = 1250, 35% below 1200; σ ? b) μ = 0.64, 12% above 0.70; σ? c) σ = 0.5, 90% above 10.0; μ = ? d) σ = 220, 3%
SAT or ACT? Each year thousands of high school students take either the SAT or ACT, standardized tests used in the college admissions process. Combined SAT scores can go as high as 1600, while the maximum ACT composite score is 36. Since the two exams use very different scales, comparisons of
Anna, a business major, took final exams in both Microeconomics and Macroeconomics and scored 83 on both. Her roommate Megan, also taking both courses, scored 77 on the Micro exam and 95 on the Macro exam. Overall, student scores on the Micro exam had a mean of 81 and a standard deviation of 5, and
Suppose that job satisfaction scores can be modeled with N(100, 12). Human resource departments of corporations are generally concerned if the job satisfaction drops below a certain score. What score would you consider to be unusually low? Explain.
Exercise 23 proposes modeling quarterly returns of a group of mutual funds with N(0.062, 0.018). The manager of this group of funds would like to flag any fund whose return is unusually low for a quarter. What level of return would you consider to be unusually low? Explain.
A survey of 200 middle managers showed a distribution of the number of hours of exercise they participated in per week with a mean of 3.66 hours and a standard deviation of 4.93 hours. a) According to the Normal model, what percent of managers will exercise fewer than one standard deviation below
A large philanthropic organization keeps records on the people who have contributed to their cause. In addition to keeping records of past giving, the organization buys demographic data on neighborhoods from the U.S. Census Bureau. Eighteen of these variables concern the ethnicity of the
Manufacturing and selling drugs that claim to reduce an individual’s cholesterol level is big business. A company would like to market their drug to women if their cholesterol is in the top 15%. Assume the cholesterol levels of adult American women can be described by a Normal model with a mean
A tire manufacturer believes that the tread life of its snow tires can be described by a Normal model with a mean of 32,000 miles and a standard deviation of 2500 miles. a) If you buy a set of these tires, would it be reasonable for you to hope that they’ll last 40,000 miles? Explain. b)
Two companies make batteries for cell phone manufacturers. One company claims a mean life span of 2 years, while the other company claims a mean life span of 2.5 years (assuming average use of minutes/month for the cell phone). a) Explain why you would also like to know the standard deviations of
The police department of a major city needs to update its budget. For this purpose, they need to under-stand the variation in their fines collected from motorists for speeding. As a sample, they recorded the speeds of cars driving past a location with a 20 mph speed limit, a place that in the past
A business publication recently released a study on the total number of years of experience in industry among CEOs. The mean is provided in the article, but not the standard deviation. Is the standard deviation most likely to be 6 months, 6 years, or 16 years? Explain which standard deviation is
Your company will admit to the executive training program only people who score in the top 3 % on the executive aptitude test discussed in Exercise 3. a) With your 2-score of 2.20, did you make the cut? b) What do you need to assume about test scores to find your answer in part a?
A newsletter for investors recently reported that the average stock price for a blue chip stock over the past 12 months was $72. No standard deviation was given. Is the standard deviation more likely to be $6, $16, or $60? Explain.
The amount of cereal that can be poured into a small bowl varies with a mean of 1.5 ounces and a standard deviation of 0.3 ounces. A large bowl holds a mean of 2.5 ounces with a standard deviation of 0.4 ounces. You open a new box of cereal and pour one large and one small bowl. a) How much more
The American Veterinary Association claims that the annual cost of medical care for dogs averages $100, with a standard deviation of $30, and for cats averages $120, with a standard deviation of $35. a) What’s the expected difference in the cost of medical care for dogs and cats? b) What’s the
In Exercise 51 we poured a large and a small bowl of cereal from a box. Suppose the amount of cereal that the manufacturer puts in the boxes is a random variable with mean 16.2 ounces and standard deviation 0.1 ounces. a) Find the expected amount of cereal left in the box. b) What’s the standard
You’re thinking about getting two dogs and a cat. Assume that annual veterinary expenses are independent and have a Normal model with the means and standard deviations described in Exercise 52. a) Define appropriate variables and express the total annual veterinary costs you may have. b) Describe
Bicycles arrive at a bike shop in boxes. Before they can be sold, they must be unpacked, assembled, and tuned (lubricated, adjusted, etc.). Based on past experience, the shop manager makes the following assumptions about how long this may take: €¢ The times for each setup phase are
The bicycle shop in Exercise 55 estimates using current labor costs that unpacking a bike costs $0.82 on average with a standard deviation of $0.16. Assembly costs $8.00 on average with a standard deviation of $0.88 and tuning costs $4.10 with a standard deviation of $0.90. Because the costs are
At a certain coffee shop, all the customers buy a cup of coffee; some also buy a doughnut. The shop owner believes that the number of cups he sells each day is normally distributed with a mean of 320 cups and a standard deviation of 20 cups. He also believes that the number of doughnuts he sells
The Atlas Body Building Company (ABC) sells “starter sets” of barbells that consist of one bar, two 20-pound weights, and four 5-pound weights. The bars weigh an average of 10 pounds with a standard deviation of 0.25 pounds. The weights average the specified amounts, but the standard deviations
A lecture hall has 200 seats with folding arm tablets, 30 of which are designed for left-handers. The typical size of classes that meet there is 188, and we can assume that about 13% of students are left-handed. Use a Normal approximation to find the probability that a right- handed student in one
The pediatrician in Exercise 4 explains to the parents that the most extreme 5% of cases often require special treatment or attention. a) Does this child fall into that group? b) What do you need to assume about the heights of 2-year-olds to find your answer to part a?
Police estimate that 80% of drivers wear their seatbelts. They set up a safety roadblock, stopping cars to check for seatbelt use. If they stop 120 cars, what’s the probability they find at least 20 drivers not wearing their seatbelt? Use a Normal approximation.
Vitamin D is essential for strong, healthy bones. Although the bone disease rickets was largely eliminated in England during the 1950s, some people there are concerned that this generation of children is at increased risk because they are more likely to watch TV or play computer games than spend
A tennis player has taken a special course to improve her serving. She thinks that individual serves are independent of each other. She has been able to make a successful first serve 70% of the time. Use a Normal approximation to find the probability she’ll make at least 65 of her first serves
Defects can occur anywhere on the wheel of a car during the manufacturing process. If X is the angle where the defect occurs, measured from a reference line, then X can be modeled as a uniform random variable on the interval from 0 to 360 degrees. a) What is the probability that the defect is found
My employee seems to leave work anytime between 5PM and 6PM, uniformly. a) What is the probability he will still be at work at 5:45 PM? b) What is the probability he will still be at work at 5:45 PM every day this week (M-F)? c) What did you assume to calculate b?
A website manager has noticed that during the evening hours, about 3 people per minute check out from their shopping cart and make an online purchase. She believes that each purchase is independent of the others. a) What model might you suggest to model the number of purchases per minute? b) What
A cell phone manufacturer samples cell phones from the assembly to test. She noticed that the number of faulty cell phones in a production run of cell phones is usually small and that the quality of one day’s run seems to have no bearing on the next day. a) What model might you use to model the
The Environmental Protection Agency (EPA) fuel economy estimates for automobiles suggest a mean of 24.8 mpg and a standard deviation of 6.2 mpg for highway driving. Assume that a Normal model can be applied. a) Draw the model for auto fuel economy. Clearly label it, showing what the 68-95-99.7 Rule
Some IQ tests are standardized to a Normal model with a mean of 100 and a standard deviation of 16. a) Draw the model for these IQ scores. Clearly label it, showing what the 68-95-99.7 Rule predicts about the scores. b) In what interval would you expect the central 95% of IQ scores to be found? c)
What percent of a standard Normal model is found in each region? Be sure to draw a picture first. a) 2 > 1.5 b) 2 < 2.25 c) -1 < 2 < 1.15 d) 121 > 0.5
An incoming MBA student took placement exams in economics and mathematics. In economics, she scored 82 and in math 86. The overall results on the economics exam had a mean of 72 and a standard deviation of 8, while the mean math score was 68, with a standard deviation of 12. On which exam did she
What percent of a standard Normal model is found in each region? Draw a picture first. a) 2 > —2.05 b) 2 < -0.33 c) 1.2 < 2 < 1.8 d) |z| < 1.28
In a standard Normal model, what value(s) of 2 cut(s) off the region described? Don’t forget to draw a picture. a) The highest 20% b) The highest 75% c) The lowest 3 % d) The middle 90%
In a standard Normal model, what value(s) of 2 cut(s) off the region described? Remember to draw a picture first. a) The lowest 12 % b) The highest 30% c) The highest 7% d) The middle 50%
Has the Consumer Price Index (CPI) fluctuated around its mean according to a Normal model? Here are some displays. Is a Normal model appropriate for these data? Explain.
For a new type of tire, a NASCAR team found the average distance a set of tires would run during a race is 168 miles, with a standard deviation of 14 miles. Assume that tire mileage is independent and follows a Normal model. a) If the team plans to change tires twice during a 500-mile race, what is
In the 4 X 100 medley relay event, four swimmers swim 100 yards, each using a different stroke. A college team preparing for the conference championship looks at the times their swimmers have posted and creates a model based on the following assumptions:€¢ The swimmers€™
Because many passengers who make reservations do not show up, airlines often overbook flights (sell more tickets than there are seats). A Boeing 767-400ER holds 245 passengers. If the airline believes the rate of passenger no-shows is 5% and sells 255 tickets, is it likely they will not have enough
Shortly after the introduction of the Belgian euro coin, newspapers around the world published articles claiming the coin is biased. The stories were based on reports that someone had spun the coin 250 times and gotten 140 heads—that’s 56% heads. a) Use the Normal model to approximate the
A cable provider wants to contact customers in a particular telephone exchange to see how satisfied they are with the new digital TV service the company has provided. All numbers are in the 452 exchange, so there are 10,000 possible numbers from 452-0000 to 452-9999. If they select the numbers with
The first Statistics exam had a mean of 65 and a stan¬dard deviation of 10 points; the second had a mean of 80 and a standard deviation of 5 points. Derrick scored an 80 on both tests. Julie scored a 70 on the first test and a 90 on the second. They both totaled 160 points on the two exams, but
In an effort to check the quality of their cell phones, a manufacturing manager decides to take a random sample of 10 cell phones from yesterday’s production run, which produced cell phones with serial numbers ranging (according to when they were produced) from 43005000 to 43005999. If each of
Indicate whether each statement below is true or false. If false, explain why. a) We can eliminate sampling error by selecting an unbiased sample. b) Randomization helps to ensure that our sample is representative. c) Sampling error refers to sample-to-sample differences and is also known as
A question posted on the Lycos website asked visitors to the site to say whether they thought that businesses should be required to pay for their employees’ health insurance. a) The population b) The population parameter of interest c) The sampling frame d) The sample e) The sampling method,
An intern for the environmental group in Exercise 3 has decided to make the survey process simpler by calling 150 of the members who attended the recent symposium on coping with climate change that was recently held in Burlington, VT. He has all the phone numbers, so it will be easy to contact
The airline company in Exercise 4 has realized that some of its customers don’t have e-mail or don’t read it regularly. They decide to restrict the mailing only to customers who have recently registered for a “Win a trip to Miami” contest, figuring that those with Internet access are more
An intern is working for Pacific TV (PTV), a small cable and Internet provider, and has proposed some questions that might be used in the survey to assess whether customers are willing to pay $50 for a new service. Question 1: If PTV offered state-of-the-art, high-speed Internet service for $50 per
Indicate whether each statement below is true or false. If false, explain why. a) A local television news program that asks viewers to call in and give their opinion on an issue typically results in a biased voluntary response sample. b) Convenience samples are generally representative of the
Indicate whether each statement below is true or false. If false, explain why. a) Asking viewers to call into an 800 number is a good way to produce a representative sample. b) When writing a survey, it’s a good idea to include as many questions as possible to ensure efficiency and to lower
For your marketing class, you’d like to take a survey from a sample of all the Catholic Church members in your city to assess the market for a DVD about Pope Francis’s first year as pope. A list of churches shows 17 Catholic churches within the city limits. Rather than try to obtain a list of
The U.S. Fish and Wildlife Service plans to study the fishing industry around Saginaw Bay. To do that, they decide to randomly select five fishing boats at the end of a randomly chosen fishing day and count the numbers and types of all the fish on those boats. a) What kind of design have they
The website www.gamefaqs.com asked, as their question of the day to which visitors to the site were invited to respond, “Do you ever read the end-user license agreements when installing software or games?" Of the 98,574 respondents, 63.47% said they never read those agreements—a fact that
Indicate whether each statement below is true or false. If false, explain why. a) To get a representative sample, you must sample a large fraction of the population. b) Using modern methods, it is best to select a representative subset of a population systematically. c) A census is the only true
Major League Baseball responding to concerns about their “brand” tests players to see whether they are using performance-enhancing drugs. Officials select a team at random, and a drug-testing crew shows up unannounced to test all 40 players on the team. Each testing day can be considered a
Pew Research Center publishes polls on issues important in the news and about American life at its website, www.pewinternet.org. At the end of a report about a survey you can find a paragraph such as this one: These readings come from a national survey conducted between November 14 and December 9,
At its website (www.gallup.com) the Gallup World Poll reports results of surveys conducted in various places around the world. At the end of one of these reports about the reliability of electric power in Africa, they describe their methods, including explanations such as the following: Results are
Pew Internet & American Life Project surveyed 802 pairs of parents and teens (aged 12-17). They report that 93% of teens have access to a computer. 25% of teens access the Internet primarily on their cell phone rather than on a computer. a) The population b) The population parameter of interest c)
The Gallup Poll interviewed 1022 randomly selected U.S. adults aged 18 and older, March 7-10, 2013. Gallup reports that when asked whether respondents thought that global warming was due primarily to human activities, 57% of respondents said it was. a) The population b) The population parameter of
Researchers waited outside a bar they had randomly selected from a list of such establishments. They stopped every tenth person who came out of the bar and asked whether he or she thought drinking and driving was a serious problem. a) The population b) The population parameter of interest c) The
Hoping to learn what issues may resonate with voters in the coming election the campaign director for a mayoral candidate selects one block at random from each of the city’s election districts. Staff members go there and interview all the residents they can find. a) The population b) The
The Environmental Protection Agency took soil samples at 16 locations near a former industrial waste dump and checked each for evidence of toxic chemicals. They found no elevated levels of any harmful substances. a) The population b) The population parameter of interest c) The sampling frame d) The
Inspectors send trained “renters” of various races and ethnic backgrounds and of both sexes to inquire about renting randomly assigned advertised apartments. They look for evidence that landlords deny access illegally based on race, sex, or ethnic background. a) The population b) The population
A company packaging snack foods maintains quality control by randomly selecting 10 cases from each day’s production and weighing the bags. Then they open one bag from each case and inspect the contents. a) The population b) The population parameter of interest c) The sampling frame d) The
An environmental advocacy group is interested in the perceptions of farmers about global climate change. Specifically, they wish to determine the percentage of organic farmers who are concerned that climate change will affect their crop yields. They use an alphabetized list of members of the
Dairy inspectors visit farms unannounced and take samples of the milk to test for contamination. If the milk is found to contain dirt, antibiotics, or other foreign matter, the milk will be destroyed and the farm is considered to be contaminated pending further testing. a) The population b) The
A local TV station conducted an “Instant Poll” to predict the winner in the upcoming mayoral election. Evening news viewers were invited to phone in their votes, with the results to be announced on the late-night news. Based on the phone calls, the station predicted that Amabo would win the
Prior to the mayoral election discussed in Exercise 31, the newspaper also conducted a poll. The paper surveyed a random sample of registered voters stratified by political party, age, sex, and area of residence. This poll predicted that Amabo would win the election with 52% of the vote. The
A local cable TV com-pany, Pacific TV (PTV), with customers in 15 towns is considering offering high-speed Internet service on its cable lines. Before launching the new service they want to find out whether customers would pay the $7 5 per month that they plan to charge. An intern has prepared
Four new sampling strategies have been proposed to help PTV determine whether enough cable subscribers are likely to purchase high-speed Internet service. For each, indicate what kind of sampling strategy is involved and what (if any) biases might result. a) Run a poll on the local TV news, asking
An amusement park has opened a new roller coaster. It is so popular that people are waiting for up to three hours for a two-minute ride. Concerned about how patrons (who paid a large amount to enter the park and ride on the rides) feel about this, they survey every tenth person in line for the
The survey of patrons waiting in line for the roller coaster in Exercise 35 asks whether they think it is worthwhile to wait a long time for the ride and whether they’d like the amusement park to install still more roller coasters. What biases might cause a problem for this survey?
The survey described in Exercise 36 asked, Many people believe this playground is too small and in need of repair. Do you think the playground should be repaired and expanded even if that means imposing an entrance fee to the park? Describe two ways this question may lead to response bias.
Examine each of the following questions for possible bias. If you think the question is biased, indicate how and propose a better question. a) Should companies that pollute the environment be compelled to pay the costs of cleanup? b) Should a company enforce a strict dress code?
An airline company is interested in the opinions of their frequent flyer customers about their proposed new routes. Specifically they want to know what proportion of them plan to use one of their new hubs in the next six months. They take a random sample of 10,000 from the database of all frequent
Examine each of the following questions for possible bias. If you think the question is biased, indicate how and propose a better question. a) Do you think that price or quality is more important in selecting a tablet computer? b) Given humanity’s great tradition of exploration, do you favor
Anytime we conduct a survey, we must take care to avoid undercoverage. Suppose we plan to select 500 names from the city phone book, call their homes between noon and 4 p.m., and interview whoever answers, anticipating contacts with at least 200 people. a) Why is it difficult to use a simple random
What about drawing a random sample only from cell phone exchanges? Discuss the advantages and disadvantages of such a sampling method compared with surveying randomly generated telephone numbers from non-cell phone exchanges. Do you think these advantages and disadvantages have changed over time?
How much change do you have on you right now? Go ahead, count it. a) Suppose you check on your change every day for a week as you head for lunch and average the results. What parameter would this average estimate? b) Suppose you ask 10 friends to average their change every day for a week, and you

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