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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
=+• Propose an ethical solution that considers the welfare of all stakeholders.
=+• What are the undesirable consequences?
=+• Identify the ethical dilemma in this scenario.
=+The Cornell National Social Survey (CNSS) is a national annual survey of a random sample of 1000 adults in the continental United States. Researchers in various disciplines can submit questions for the survey. According to the Cornell Survey Research Institute’s site,
=+e) What’s the probability that she hits the bull’s-eye more often than she misses?
=+d) What’s the probability that there are exactly 8 bull’s-eyes?
=+c) What’s the probability that there are no more than 8 bull’s-eyes?
=+b) What’s the probability that she never misses?
=+a) Find the mean and standard deviation of the number of bull’s-eyes she may get.
=+60. Still more arrows. Suppose the archer from Exercise 58 shoots 10 arrows.
=+e) What’s the probability that the majority is righthanded?
=+) What’s the probability that there are exactly 6 of each?
=+c) What’s the probability that there are no more than 10 righties?
=+b) What’s the probability that they’re not all righthanded?
=+a) Find the mean and standard deviation of the number of right-handers in the group.
=+59. Still more lefties. Suppose we choose 12 people instead of the 5 chosen in Exercise 57
=+c) If she keeps shooting arrows until she hits the bull’s-eye, how long do you expect it will take?
=+b) With what standard deviation?
=+a) How many bull’s-eyes do you expect her to get?
=+58. More arrows. Consider our archer from Exercise 52.
=+c) If we keep picking people until we find a lefty, how long do you expect it will take?
=+b) With what standard deviation?
=+a) How many lefties do you expect?
=+57. Lefties, redux. Consider our group of 5 people from Exercise 51.
=+c) If the mean number of faulty cell phones is 2 per day, what is the probability that 3 or more faulty cell phones were produced in today’s run?M06_SHAR8696_03_SE_C06.indd 235 14/07/14 7:26 AM 236 CHAPTER 6 Random Variables and Probability Models
=+b) If the mean number of faulty cell phones is 2 per day, what is the probability that no faulty cell phones will be produced tomorrow?
=+a) What model might you use to model the number of faulty cell phones produced in one day?
=+56. Quality control. 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.
=+c) What is the probability that no one makes a purchase in the next 2 minutes?
=+b) What is the probability that in any 1 minute at least one purchase is made?
=+a) What model might you suggest to model the number of purchases per minute?
=+55. Web visitors. 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.
=+d) What is the probability that the first two cell phones are both from the last 100 to be produced?
=+c) What is the probability that the first cell phone selected is either from the last 200 to be produced or from the first 50 to be produced?
=+b) What is the probability that a randomly selected cell phone will be one of the last 100 to be produced?
=+a) What distribution would they use to model the selection?
=+54. Manufacturing quality. 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
=+c) What is the probability the number selected will end in 000?
=+b) What is the probability the number selected will be an even number?
=+a) What distribution would they use to model the selection?
=+53. Satisfaction survey. An internet provider wants to contact customers in a particular telephone exchange to see how satisfied they are with the improved download speed the company has provided. All numbers are in the 62 exchange, so there are 10,000 possible numbers from 62-0000 to 62-9999.
=+52. Arrows. 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
=+51. Lefties. 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
=+d) What is the probability of going three years in a row without a major hurricane?
=+c) What is the probability of having a year with no major hurricanes?
=+b) What is the standard deviation of the annual frequency of major hurricanes?
=+a) What is the mean number of major hurricanes per year?
=+50. Hurricane insurance, part 2. 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.
=+49. Hurricane insurance. 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
=+b) What is the standard deviation of stops per hour?
=+a) What is the mean number of stops per hour?
=+48. Bean bags. Cellophane that is going to be formed into bags for items such as dried beans or bird seed is passed over a light sensor to test if the alignment is correct before it passes through the heating units that seal the edges.Small adjustments can be made by the machine automatically.
=+d) What is the probability that a 2 ft by 3 ft screen will be replaced because it has too many defects?
=+c) What is the probability that a 2 ft by 3 ft screen will have at least one defect?M06_SHAR8696_03_SE_C06.indd 234 14/07/14 7:26 AM Exercises 235
=+b) What is the standard deviation of blank pixels per square foot?
=+a) What is the mean number of blank pixels per square foot?
=+47. Missing pixels. 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
=+46. Credit cards. College students are a major target for advertisements for credit cards. At a university, 65% of students surveyed said they had opened a new credit card account within the past year. If that percentage is accurate, how many students would you expect to survey before finding
=+45. Side effects. Researchers testing a new medication find that 7% of users have side effects. To how many patients would a doctor expect to prescribe the medication before finding the first one who has side effects?
=+c) The first bad chip they find will be the fourth one they test.d) The first bad chip they find will be one of the first three they test.
=+a) The fifth chip they test is the first bad one they find.b) They find a bad one within the first 10 they examine.
=+44. Computer chip manufacturer. 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.
=+d) The first presentation he closes will be on one of his first three attempts.
=+c) The first presentation he closes will be on his second attempt.
=+43. Closing sales. 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.
=+d) An executive reads that 74% of employees in his industry are dissatisfied with their jobs. How many dissatisfied employees can he expect to find among the 481 employees in his company?
=+c) A city council of 11 Republicans and 8 Democrats picks a committee of 4 at random. How likely are they to choose all Democrats?
=+37 of these dolls to the local toy store. How likely are they to find any buttons not properly attached?
=+b) A manufacturer recalls a doll because about 3% have buttons that are not properly attached. Customers return
=+a) You survey 500 potential customers to determine their color preference.
=+42. Bernoulli, part 2. Can we use probability models based on Bernoulli trials to investigate the following situations?Explain.
=+e) A company realizes that about 10% of its packages are not being sealed properly. In a case of 24 packages, how likely is it that more than 3 are unsealed?
=+d) We poll 500 of the 3000 stockholders to see how likely it is that the proposed budget will pass.
=+c) From a workforce of 13 men and 23 women, all five promotions go to men. How likely is that, if promotions are based on qualifications rather than gender?
=+b) A medical research lab has samples of blood collected from 120 different individuals. How likely is it that the majority of them are Type A blood, given that Type A is found in 43% of the population?
=+a) Each week a doctor rolls a single die to determine which of his six office staff members gets the preferred parking space.
=+41. Bernoulli. Can we use probability models based on Bernoulli trials to investigate the following situations? Explain.
=+d) Do you have to assume independence for the repairs and sale prices of the houses? Explain.
=+b) Find the mean (expected value) of the net profit.c) Find the standard deviation of the net profit.
=+a) Define your random variables, and use them to create a random variable for the broker’s net profit.
=+40. Real estate. A real-estate broker in the university town of Maastricht, in the Netherlands, purchased 3 two-bedroom houses in a depressed market for a combined cost of $500,000. He expects the cleaning and repair costs on each house to average $50,000 with a standard deviation of $5,000.
=+d) Do you have to assume independence for the sales on eBay? Explain.
=+c) Find the standard deviation of the net revenue.
=+b) Find the mean (expected value) of the net revenue.
=+a) Define your random variables, and use them to create a random variable for the collector’s net revenue.
=+39. eBay. An Australian collector purchased a quantity of cricket cards and is going to sell them on eBay. He has 19 Ashes Cricket Card sets. In recent auctions, the mean selling price of such cards has been $12.11, with a standard deviation of $1.38. He also has 13 Australian Champion
=+c) Should she buy the stock option? Discuss the pros and cons in terms of your answers to (a) and (b).M06_SHAR8696_03_SE_C06.indd 233 14/07/14 7:26 AM 234 CHAPTER 6 Random Variables and Probability Models
=+b) What is the standard deviation of her gain?
=+a) How much does she expect to gain?
=+38. Day trading. 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
=+b) What is the standard deviation?
=+a) If she books the cheaper flight, what can she expect to gain, on average?
=+37. Cancelled flights. 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
=+How about the standard deviation?
=+d) Do you need to make any assumptions in calculating the mean?
=+c) Find the standard deviation of the net income.
=+b) Find the mean of the net income.
=+a) Define your random variables, and use them to express the farmer’s net income.
=+36. Farmers’ market. 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
=+d) Do you need to make any assumptions in calculating the mean? How about the standard deviation?
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