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

Respond to the following questions: a) After an unusually dry autumn, a radio announcer is heard to say, “Watch out! We’ll pay for these sunny days later on this winter.” Explain what he’s trying to say, and comment on the validity of his reasoning. b) A batter who had failed to get a hit
Even though commercial airlines have excellent safety records, in the weeks following a crash, airlines often report a drop in the number of passengers, probably because people are afraid to risk flying. a) A travel agent suggests that since the law of averages makes it highly unlikely to have two
Indicate which of the following represent independent events. Explain briefly. a) Prices of houses on the same block. b) Successive measurements of your heart rate as you exercise on a treadmill. c) Measurements of the heart rates of all students in the gym.
An investment newsletter makes general predictions about the economy to help their clients make sound investment decisions. a) Recently they said that because the stock market had been up for the past three months in a row that it was “due for a correction” and advised their client to reduce
Insurance companies collect annual payments from homeowners in exchange for paying to rebuild houses that burn down. a) Why should you be reluctant to accept a $300 payment from your neighbor to replace his house should it burn down during the coming year? b) Why can the insurance company make that
Recently, the International Gaming Technology company issued the following press release: (LAS VEGAS, Nev.)—Cynthia Jay was smiling ear to ear as she walked into the news conference at the Desert Inn Reson in Las Vegas today, and well she should. Last night, the 37-year-old cocktail waitress won
A toy company is preparing to market an electronic game for young children that €œrandomly€ generate a color. They suspect, however, that the way the random color is determined may not be reliable, so they ask the programmers to perform tests and report the frequencies of each
Many stores run €œsecret sales€: Shoppers receive cards that determine how large a discount they get, but the percentage is revealed by scratching off that black stuff (what is that?) only after the purchase has been totaled at the cash register. The store is required to reveal
A tire manufacturer recently announced a recall because 2% of its tires are defective. If you just bought a new set of four tires from this manufacturer, what is the probability that at least one of your new tires is defective?
For a sales promotion, the manufacturer places winning symbols under the caps of 10% of all Pepsi bottles. If you buy a six-pack of Pepsi, what is the probability that you win something?
In developing their warranty policy, an automobile company estimates that over a 1-year period 17% of their new cars will need to be repaired once, 7% will need repairs twice, and 4% will require three or more repairs. If you buy a new car from them, what is the probability that your car will
You work for a large global management consulting company. Of the entire work force of analysts, 55% have had no experience in the telecommunications industry, 32% have had limited experience (less than 5 years), and the rest have had extensive experience (5 years or more). On a recent project, you
Consider again the auto repair rates described in Exercise 27. If you bought two new cars, what is the probability that: a) Neither will need repair? b) Both will need repair? c) At least one car will need repair?
In many state lotteries, you can choose which numbers to play. Consider a common form in which you choose 5 numbers. Which of the following strategies can improve your chance of winning? If the method works, explain why. If not, explain why using appropriate statistics terms. a) Always play 1, 2,
You are assigned to be part of a team of three analysts of a global management consulting company as described in Exercise 28. What is the probability that of your other two teammates: In Exercise, You work for a large global management consulting company. Of the entire work force of analysts, 55%
You used the Multiplication Rule to calculate repair probabilities for your cars in Exercise 29.a) What must be true about your cars in order to make that approach valid?b) Do you think this assumption is reasonable? Explain.
In a sample of real estate ads, 64% of homes for sale had garages, 21% have swimming pools, and 17% have both features. What is the probability that a home for sale has? a) A pool, a garage, or both? b) Neither a pool nor a garage? c) A pool but no garage?
Employment data at a large company reveal that 72% of the workers are married, 44% are college graduates, and half of the college grads are married. What’s the probability that a randomly chosen worker is? a) Neither married nor a college graduate? b) Married but not a college graduate? c)
The Mars Company says that before the introduction of purple, yellow made up 20% of their plain M&M candies, red made up another 20%, and orange, blue, and green each made up 10%. The rest were brown. a) If you picked an M&M at random from a pre-purple bag of candies, what is the probability that
The American Red Cross must track their supply and demand for various blood types. They estimate that about 45% of the U.S. population has Type O blood, 40% Type A, 11 % Type B, and the rest Type AB- a) If someone volunteers to give blood, what is the probability that this donor: i) Has Type AB
In Exercise 35, you calculated probabilities of getting various colors of M&M’s. a) If you draw one M&M, are the events of getting a red one and getting an orange one disjoint or independent or neither? b) If you draw two M&M’s one after the other, are the events of getting a red on the first
In Exercise 36, you calculated probabilities involving various blood types. a) If you examine one donor, are the events of the donor being Type A and the donor being Type B disjoint or independent or neither? Explain your answer. b) If you examine two donors, are the events that the first donor is
A recent study of IRS audits showed that, for estates worth less than $5 million, about 1 out of 7 of all estate tax returns are audited, but that probability increases to 50% for estates worth over $5 million. Suppose a tax accountant has three clients who have recently filed returns for estates
For the same kind of lottery as in Exercise 3, which of the following strategies can improve your chance of winning? If the method works, explain why. If not, explain why using appropriate statistics terms. a) Choose randomly from among the numbers that have not come up in the last 3 lottery
Because gambling is big business, calculating the odds of a gambler winning or losing in every game is crucial to the financial forecasting for a casino. A standard slot machine has three wheels that spin independently. Each has 10 equally likely symbols: 4 bars, 3 lemons, 2 cherries, and a bell.
A company has recently replaced their e-mail spam filter because investigations had found that the volume of spam e-mail was interrupting productive work on about 15 % of workdays. To see how bad the situation was, calculate the probability that during a 5-day work week, e-mail spam would interrupt
The technical support desk at a college has set up a special service for tablets. A survey shows that 54% of tablets on campus run Apple’s iOS, 43% run Google’s Android OS, and 3% run Microsoft’s Windows. Assuming that users of each of the operating systems are equally likely to call in for
In addition to slot machines, casinos must understand the probabilities involved in card games. Suppose you are playing at the blackjack table, and the dealer shuffles a deck of cards. The first card shown is red. So is the second and the third. In fact, you are surprised to see 5 red cards in a
A shipment of road bikes has just arrived at The Spoke, a small bicycle shop, and all the boxes have been placed in the back room. The owner asks her assistant to start bringing in the boxes. The assistant sees 20 identical looking boxes and starts bringing them into the shop at random. The owner
A Gallup Poll in March 2013 (www.gallup.com/poll/110821/gallup-daily-us-economic-conditions.aspx) asked 1500 U.S. adults to rate economic conditions in the country today as “excellent,” “good,” “only fair,” or “poor.” The results are below:If we select a person at random from this
Exercise 45 shows the results of a Gallup Poll about U.S. economic conditions. Suppose we select three adults at random from this sample. a) What is the probability that all three responded “Poor”? b) What is the probability that none responded “Poor”? c) What assumption did you make in
The General Social Survey, run annually, asked respondents €œDo you have in your home (or garage) any guns or revolvers?€ The responses are given in the table. (sda.berkeley.edu/cgi-bin/hsda?harcsda+gssl0)a) If we select a random person from this sample of 1270 adults, what is
Exercise 47 shows the results of a poll that asked about gun ownership. Suppose we select three adults at random from this sample. a) What is the probability that all three respond “Yes”? b) What is the probability that none responded “Yes”? c) What assumption did you make in computing
As manager for a construction firm, you are in charge of bidding on two large contracts. You believe the probability you get contract #1 is 0.8. If you get contract #1, the probability you also get contract #2 will be 0.2, and if you do not get #1, the probability you get #2 will be 0.4.a) Sketch
A recent survey found that, despite airline requests, about 40% of passengers don’t fully turn off their cell phones during takeoff and landing (although they may put them in “airplane mode”). The two passengers across the aisle (in seats A and B) clearly do not know each other. a) What is
A company that manufactures and sells consumer video cameras sells two versions of their popular hard disk camera, a basic camera for $750, and a deluxe version for $1250. About 75% of customers select the basic camera. Of those, 60% purchase the extended warranty for an additional $200. Of the
According to the Pew 2012 News Consumption survey, 50% of adults who post news on Twitter (“tweet”) are younger than 30. But according to the U.S. Census, only 23% of adults are less than 30 years old. A separate survey by Pew in 2012 found that 15% of adults tweet. a) Find the probability that
Of the 2201 people on the RMS Titanic, only 711 survived. The practice of €œwomen and children first€ was first used to describe the chivalrous actions of the sailors during the sinking of the HMS Birkenhead in 1852, but became popular after the sinking of the Titanic, during
A 2011 Mintel report on coffeehouses asked consumers if they were spending more time in coffeehouses. The table below gives the responses classified by age:a) What is the probability that a randomly selected respondent is spending more time at coffeehouses and donut shops this year than last
A Mintel study asked consumers if electronic communications devices influenced whether or not they bought a certain car. The table on the next page gives the results classified by household income:If we select a person at random from this sample:a) What is the probability that electronic
Exercises 36 and 38 discussed the challenges faced by the Red Cross in finding enough blood of various types. But blood typing also depends on the Rh factor, which can be negative or positive. Here is a table of the estimated proportions worldwide for blood types categorized on both type and Rh
A U.S. pharmaceutical company is considering manufacturing and marketing a pill that will help to lower both an individual€™s blood pressure and cholesterol. The company is interested in understanding the demand for such a product. The joint probabilities that an adult American man has high
A European department store is developing a new advertising campaign for their new U.S. location, and their marketing managers need to understand their target market better. A survey of adult shoppers found the probabilities that an adult would shop at their new U.S. store classified by age is
At your school, 10% of the class are marketing majors. If you are randomly assigned to two partners in your statistics class, a) What is the probability that the first partner will be a marketing major? b) What is the probability that the first partner won’t be a marketing major? c) What is the
Look again at the data from the coffeehouse survey in Exercise 53. a) If we select a person at random, what’s the probability we choose a person between 18 and 24 years old who is spending more at coffeehouses? b) Among the 18- to 24-year olds, what is the probability that the person responded
Look again at the data in the electronic communications in Exercise 54. a) If we select a respondent at random, what’s the probability that we choose a person earning less than $50 K and responded “somewhat”? b) Among those earning $50-99.9K, what is the probability that the person responded
In the real estate research described in Exercise 33, 64% of homes for sale have garages, 21% have swimming pools, and 17% have both features.a) What is the probability that a home for sale has a garage, but not a pool?b) If a home for sale has a garage, what’s the probability that it has a pool,
Professional polling organizations face the challenge of selecting a representative sample of U.S. adults by telephone. This has been complicated by people who only use cell phones and by others whose landline phones are unlisted. A careful survey by Democracy Corps determined the following
The following table shows a sample of property listings and values from one neighborhood (one ZIP code) in the Washington, DC, area in December 2011:a) In this sample, what proportion of homes is valued at $500K or less? b) Are the number of bedrooms and property values independent? Explain.
A business student is searching for a used car to purchase, so she posts an ad to a website saying she wants to buy a used Jeep between $18,000 and $20,000. From Kelly€™s BlueBook.com, she learns that there are 149 cars matching that description within a 30-mile radius of her home. If we assume
The CEO of a mid-sized company has to relocate to another part of the country. To make it easier, the company has hired a relocation agency to help purchase a house. The CEO has 5 children and so has specified that the house have at least 5 bedrooms, but hasn€™t put any other constraints on the
Laptop Computers have been growing in popularity according to a study by Current Analysis Inc. Laptops now represent more than half the computer sales in the United States. A campus bookstore sells both types of computers and in the last semester sold 56% laptops and 44% desktops. Reliability rates
The following contingency table shows opinion about global warming among U.S. adults, broken down by political party affiliation (based on a poll in October 2012 by Pew Research found at www.people-press.org/2012/10/15/more-say-there-is-solid-evidence-of-global-warming/).a) What is the probability
Multigenerational families can be categorized as having two adult generations such as parents living with adult children, €œskip€ generation families, such as grandparents living with grandchildren, and three or more generations living in the household. Pew Research surveyed
Using the table from Exercise 7,a) What is the probability that a randomly selected U.S. adult who is a Republican believes that global warming is a serious issue?b) What is the probability that a randomly selected U.S. adult is a Republican given that he or she believes global warming is a serious
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) X €“ 20b) 0.5Tc) X + Yd) X-Y
A broker has calculated the expected values of two different financial instruments X and Y. Suppose that E(X) = $100, E (Y) = $90, SD (X) = $12, and SD (Y) — $8. Find each of the following. a) £ (X+ 10) and SD (X + 10) b) E (5Y) and SD (5Y) c) E (X+ Y) and SD (X + Y) d) What assumption must you
A company selling glass ornaments by mail-order expects, from previous history, that 6% of the ornaments it ships will break in shipping. You purchase two ornaments as gifts and have them shipped separately to two different addresses. What is the probability that both arrive safely? What did you
Which of these situations fit the conditions for using Bernoulli trials? Explain. a) You are rolling 5 dice and need to get at least two 6s to win the game. b) We record the distribution of home states of customers visiting our website. c) A committee consisting of 11 men and 8 women selects a
At the airport entry sites, a computer is used to randomly decide whether a traveler’s baggage should be opened for inspection. If the chance of being selected is 12%, can you model your chance of having your baggage opened with a Bernoulli model? Check each of the conditions specifically.
The U.S. Census Bureau’s 2007 Survey of Business Owners showed that 28.7% of all non-farm businesses are owned by women. You are phoning local businesses and assume that the national percentage is true in your area. You wonder how many calls you will have to make before you find one owned by a
A manufacturer of clothing knows that the probability of a button flaw (broken, sewed on incorrectly, or missing) is 0.002. An inspector examines 50 shirts in an hour, each with 6 buttons. Using a Poisson probability model:a) What is the probability that she finds no button flaws?b) What is the
Replacing the buttons with snaps increases the probability of a flaw to 0.003, but the inspector can check 70 shirts an hour (still with 6 snaps each). Now what is the probability she finds no snap flaws?
The probability model below describes the number of repair calls that an appliance repair shop may receive during an hour.a) How many calls should the shop expect per hour?b) What is the standard deviation?
A small software company will bid on a major contract. It anticipates a profit of $50,000 if it gets it, but thinks there is only a 30% chance of that happening. a) What’s the expected profit? b) Find the standard deviation for the profit.
A commuter must pass through five traffic lights on her way to work and will have to stop at each one that is red. After keeping a record for several months, she developed the following probability model for the number of red lights she hits:a) How many red lights should she expect to hit each
A consumer organization inspecting new cars found that many had appearance defects (dents, scratches, paint chips, etc.). While none had more than three of these defects, 7% had three, 11 % had two, and 21 % had one defect.a) Find the expected number of appearance defects in a new car.b) What is
A sporting goods manufacturer was asked to sponsor a local boy in two fishing tournaments. They claim the probability that he will win the first tournament is 0.4. If he wins the first tournament, they estimate the probability that he will also win the second is 0.2. They guess that if he loses the
Your company bids for two contracts. You believe the probability that you get contract #1 is 0.8. If you get contract #1, the probability that you also get contract #2 will be 0.2, and if you do not get contract #1, the probability that you get contract #2 will be 0.3.a) Are the outcomes of the two
A company has discovered that a recent batch of batteries had manufacturing flaws, and has issued a recall. You have 10 batteries covered by the recall, and 3 are dead. You choose 2 batteries at random from your package of 10.a) Has the assumption of independence been met? Explain.b) Create a
A grocery supplier believes that the mean number of broken eggs per dozen is 0.6, with a standard deviation of 0.5. You buy 3 dozen eggs without checking them. a) How many broken eggs do you expect to get? b) What’s the standard deviation? c) Is it necessary to assume the cartons of eggs are
A commuter finds that she waits an average of 14.8 seconds at each of five stoplights, with a standard deviation of 9.2 seconds. Find the mean and the standard deviation of the total amount of time she waits at all five lights. What, if anything, did you assume?
For warranty purposes, analysts want to model the number of defects on a screen of the new tablet they are manufacturing. Let X = the number of defective pixels per screen. If X can be modeled by:a) What is the expected number of defective pixels per screen? b) What is the standard deviation of the
Suppose that the appliance shop in Exercise 23 plans an 8-hour day. a) Find the mean and standard deviation of the number of repair calls they should expect in a day. b) What assumption did you make about the repair calls? c) Use the mean and standard deviation to describe what a typical 8-hour day
At a casino, people play the slot machines in hopes of hitting the jackpot, but most of the time, they lose their money. A certain machine pays out an average of $0.92 (for every dollar played), with a standard deviation of $120. a) Why is the standard deviation so large? b) If a gambler plays 5
A bicycle shop plans to offer 2 specially priced children’s models at a sidewalk sale. The basic model will return a profit of $120 and the deluxe model $150. Past experience indicates that sales of the basic model will have a mean of 5.4 bikes with a standard deviation of 1.2, and sales of the
A farmer has 100 lb of apples and 50 lb of potatoes for sale. The market price for apples (per pound) each day is a random variable with a mean of 0.5 dollars and a standard deviation of 0.2 dollars. Similarly, for a pound of potatoes, the mean price is 0.3 dollars and the standard deviation is 0.1
Mary is deciding whether to book the cheaper flight home college after her final exams, but she’s unsure when her last exam will be. She thinks there is only a 20% chance that the exam will be scheduled after the last day she can get a seat on the cheaper flight. If it is and she has to cancel
An option to buy a stock is priced at $200. If the stock closes above 30 on May 15, the option will be worth $1000. If it closes below 20, the option will be worth nothing, and if it closes between 20 and 30 (inclusively), the option will be worth $200. A trader thinks there is a 50% chance that
A collector purchased a quantity of action figures and is going to sell them on eBay. He has 19 Hulk figures. In recent auctions, the mean selling price of similar figures has been $12.11, with a standard deviation of $1.38. He also has 13 Iron Man figures which have had a mean selling price of
A day trader buys an option on a stock that will return $100 profit if the stock goes up today and lose $400 if it goes down. If the trader thinks there is a 75% chance that the stock will go up, a) What is her expected value of the option’s profit? b) What do you think of this option?
A real-estate broker in Washington, DC, purchased 3 two-bedroom houses in a depressed market for a combined cost of $1,000,000. He expects the cleaning and repair costs on each house to average $100,000 with a standard deviation of $15,000. When he sells them, after subtracting taxes and other
Can we use probability models based on Bernoulli trials to investigate the following situations? Explain. a) Each week a doctor rolls a single die to determine which of his six office staff members gets the preferred parking space. b) A medical research lab has samples of blood collected from 120
Can we use probability models based on Bernoulli trials to investigate the following situations? Explain. a) You survey 500 potential customers to determine their color preference. b) A manufacturer recalls a doll because about 3% have buttons that are not properly attached. Customers return 37 of
A salesman normally makes a sale (closes) on 80% of his presentations. Assuming the presentations are independent, find the probability of each of the following. a) He fails to close for the first time on his fifth attempt. b) He closes his first presentation on his fourth attempt. c) The first
Suppose a computer chip manufacturer rejects 2% of the chips produced because they fail presale testing. Assuming the bad chips are independent, find the probability of each of the following. a) The fifth chip they test is the first bad one they find. b) They find a bad one within the first 10 they
A company that manufactures large LCD screens knows that not all pixels on their screen light, even if they spend great care when making them. In a sheet 6 ft by 10 ft (72 in. by 120 in.) that will be cut into smaller screens, they find an average of 4.7 blank pixels. They believe that the
An insurance company needs to assess the risks associated with providing hurricane insurance. During the 22 years from 1990 through 2011, Florida was hit by 27 major hurricanes (level 3 and above). If hurricanes are independent and the mean has not changed, what is the probability of having a year
During the 18 years from 1995 through 2012, there were 144 hurricanes in the Atlantic basin. Assume that hurricanes are independent and the mean has not changed. a) What is the mean number of major hurricanes per year? b) What is the standard deviation of the annual frequency of major
A manufacturer of game controllers is concerned that their controller may be difficult for left-handed users. They set out to find lefties to test. About 13 % of the population is left-handed. If they select a sample of five customers at random in their stores, what is the probability of each of
An Olympic archer is able to hit the bull’s-eye 80% of the time. Assume each shot is independent of the others. If she shoots 6 arrows, what’s the probability of each of the following results? a) Her first bull’s-eye comes on the third arrow. b) She misses the bull’s-eye at least once. c)
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
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
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 and wants to model the number of purchases per minute. a) What model might you suggest
The manufacturer in Exercise 54 has 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 number of faulty cell phones produced in
Consider our group of 5 people from Exercise 51. a) How many lefties do you expect? b) With what standard deviation? c) If we keep picking people until we find a lefty, how long do you expect it will take?
Consider our archer from Exercise 52. a) How many bull’s-eyes do you expect her to get? b) With what standard deviation? c) If she keeps shooting arrows until she hits the bull’s-eye, how long do you expect it will take?
Suppose we choose 12 people instead of the 5 chosen in Exercise 57 a) Find the mean and standard deviation of the number of right-handers in the group. b) What’s the probability that they’re not all right- handed? c) What’s the probability that there are no more than 10 righties? d) What’s
Suppose the archer from Exercise 58 shoots 10 arrows. a) Find the mean and standard deviation of the number of bull’s-eyes she may get. b) What’s the probability that she never misses? c) What’s the probability that there are no more than 8 bull’s-eyes? d) What’s the probability that
An orthodontist has three financing packages, and each has a different service charge. He estimates that 30% of patients use the first plan, which has a $10 finance charge; 50% use the second plan, which has a $2 0 finance charge; and 20% use the third plan, which has a $30 finance charge. a) Find

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