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business
business statistics in practice
Business Statistics Plus Pearson Mylab Statistics With Pearson Etext 3rd Edition Norean R Sharpe ,Richard D De Veaux ,Paul Velleman - Solutions
=+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 their holdings. What “law” are they applying? Comment.
=+b) They advised buying a stock that had gone down in the past four sessions because they said that it was clearly “due to bounce back.” What “law” are they applying? Comment.
=+21. Fire insurance. 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 offer?
=+22. Casino gambling. 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 Resort in Las Vegas today, and well she should. Last night, the 37-year-old
=+a) How can the Desert Inn afford to give away millions of dollars on a $3 bet?
=+b) Why did the company issue a press release? Wouldn’t most businesses want to keep such a huge loss quiet?
=+23. Toy company. A toy company is preparing to market an electronic game for young children that “randomly” generates 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
=+24. Store discounts. Many stores run “secret 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
=+25. Quality control. 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?
=+26. Pepsi promotion. 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?
=+27. Auto warranty. 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
=+28. Consulting team. 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).
=+a) Extensive telecommunications experience?
=+b) Some telecommunications experience?
=+c) No more than limited telecommunications experience?
=+29. Auto warranty, part 2. 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?
=+30. Consulting team, part 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:a) Neither has any telecommunications experience?b) Both have some
=+31. Auto warranty, again. 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.
=+32. Final consulting team project. You used the Multiplication Rule to calculate probabilities about the telecommunications experience of your consulting teammates in Exercise 30.
=+a) What must be true about the groups in order to make that approach valid?
=+b) Do you think this assumption is reasonable? Explain.
=+33. Real estate. 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?
=+34. Human resource data. 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) Married or a college graduate?
=+35. Mars product information. 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 it was:i) Brown?ii) Yellow or orange?iii) Not green?iv) Striped?
=+b) Assuming you had an infinite supply of M&M’s with the older color distribution, if you picked three M&M’s in a row, what is the probability that:
=+i) They are all brown?
=+ii) The third one is the first one that’s red?iii) None are yellow?
=+iv) At least one is green?
=+36. American Red Cross. 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 blood?ii) Has Type A or Type B blood?iii) Is not Type O?
=+b) Among four potential donors, what is the probability that:i) All are Type O?ii) None have Type AB blood?iii) Not all are Type A?
=+iv) At least one person is Type B?
=+37. More Mars product information. 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 and a red on the second disjoint or independent or neither?
=+c) Can disjoint events ever be independent? Explain.
=+38. American Red Cross, part 2. 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 Type A and the second donor is Type B disjoint or independent or neither?
=+c) Can disjoint events ever be independent? Explain.
=+39. Tax accountant. 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
=+a) All three will be audited?b) None will be audited?c) At least one will be audited?
=+d) What did you assume in calculating these probabilities?
=+40. Casinos. 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. If you play once, what is the probability that you will get:a) 3 lemons?b) No fruit symbols?c) 3 bells (the jackpot)?d) No bells?
=+e) At least one bar (an automatic loser)?
=+41. Spam filter. 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
=+a) On Monday and again on Tuesday?
=+b) For the first time on Thursday?c) Every day?
=+d) At least once during the week?
=+42. Tablet tech support. 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
=+a) All are iOS?b) None are Android?
=+c) At least one is a Windows machine?d) All are Windows machines?
=+43. Casinos, part 2. 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
=+a) Are you correct in thinking that there’s a higher probability that the next card will be black than red? Explain.
=+b) Is this an example of the Law of Large Numbers? Explain.
=+44. Inventory. 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 identicallooking boxes and starts bringing them into the shop at
=+a) Is she correct in thinking that there’s a higher probability that the next box will contain a men’s bike? Explain.
=+b) Is this an example of the Law of Large Numbers? Explain.
=+45. Brazil’s future economic situation. As part of the Pew Research Global Attitudes project, people from 39 countries are asked the question ‘Do you expect our country’s economic situation to improve, remain the same or worsen in the next year?’ As can be seen from the table, in 2013,
=+If we select a person at random from this Brazilian sample of adults:
=+a) What is the probability that the person foresees an improving economy?
=+b) What is the probability that the person foresees a stable economy or better?
=+46. More on Brazil’s future economic situation. Exercise 45 shows responses from a Brazilian sample about the country’s future economic situation. Suppose we select three adults at random from this sample.
=+a) What is the probability that all three responded “Improve”?
=+b) What is the probability that none responded “Improve”?
=+c) What assumption did you make in computing these probabilities?
=+d) Explain why you think that assumption is reasonable.
=+47. Mobile Technology in South Africa. According to the Pew Research report Emerging Nations Embrace Internet, Mobile Technology, emerging and developing countries adopt modern communication technology very rapidly, (http://www.pewglobal.org/2014/02/13/). South Africa is an example of such a
=+a) If we select a random person from this sample of South African adults, what is the probability they own a smartphone?
=+b) What is the probability of owning a cell phone that is not a smartphone?
=+c) Are there more smartphones, or regular cell phones in South Africa?
=+48. Mobile Technology in South Africa, part 2. Exercise 47 shows the results of a poll that asked about cell phone ownership in South Africa. Suppose we select three adults at random from this sample.
=+a) What is the probability that all three own a smartphone?
=+b) What is the probability that none owns a smartphone?
=+c) What assumption did you make in computing these probabilities?
=+d) Explain why you think that assumption is reasonable.
=+49. Contract bidding. 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
=+b) What is the probability you will get both contracts?
=+c) Your competitor hears that you got the second contract but hears nothing about the first contract. Given that you got the second contract, what is the probability that you also got the first contract?
=+50. Extended warranties. 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
=+a) Sketch the probability tree for total purchases.
=+b) What is the percentage of customers who buy an extended warranty?
=+c) What is the expected revenue of the company from a camera purchase (including warranty if applicable)?
=+d) Given that a customer purchases an extended warranty,
=+what is the probability that he or she bought the deluxe version?
=+51. Tweeting. 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 a random adult is both less than 30 years old and a Twitter poster. That is, find P(Tweet and 630).
=+b) For a random young 16302 adult, what is the probability he or she is a tweeter? That is, find P1Tweet 6302(Hint: use Bayes theorem.)
=+52. Titanic survival. Of the 2201 people on the RMS Titanic, only 711 survived. The practice of “women 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,
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