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business
business statistics in practice

Questions and Answers of Business Statistics In Practice

=+42. Low return. 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
=+41. Low job satisfaction. 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
=+40. Economics. 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
=+the combined SAT can be modeled by N(1000, 200) and the ACT can be modeled by N(27, 3). If an applicant to a university has taken the SAT and scored 1260 and another student has taken the ACT and
=+39. 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
=+38. Parameters, again. 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
=+37. Parameters. 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
=+b) What IQ represents the 98th percentile?c) What’s the IQR of the IQs?
=+a) What IQ represents the 15th percentile?
=+36. IQs, finis. Consider the IQ model N(100, 16) one last time.
=+c) What’s the IQR of the quarterly returns for this group of funds?
=+b) What value represents the 99th percentile?
=+a) What value represents the 40th percentile of these returns?
=+35. Mutual funds, finis. Consider the Normal model N(0.062, 0.018) for returns of mutual funds in Exercise 23 one last time.
=+34. More IQs. In the Normal model N(100, 16) for IQ scores from Exercise 24, what cutoff value bounds thea) highest 5% of all IQs?b) lowest 30% of the IQs?c) middle 80% of the IQs?d) lowest 90% of
=+33. Mutual funds, once more. Based on the model N(0.062, 0.018) for quarterly returns from Exercise 23, what are the cutoff values for thea) highest 10% of these funds?b) lowest 20%?c) middle
=+32. Normal IQs. Based on the Normal model N (100, 16)describing IQ scores from Exercise 24, what percent of applicants would you expect to have scoresa) over 80?b) under 90?c) between 112 and
=+31. Mutual fund probabilities. 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
=+what cutoff value of price would separate thea) lowest 16% of the days?b) highest 0.15%?c) middle 68%?d) highest 50%?
=+30. Stock prices, again. According to the model in Exercise 28,
=+29. Currency exchange rates, again. For the model of the EUR/GBP exchange rate discussed in Exercise 27, what would the cutoff rates be that would separate thea) highest 16% of EUR/GBP rates?b)
=+a) above $205.08?M07_SHAR8696_03_SE_C07.indd 264 14/07/14 7:31 AM Exercises 265b) below $212.24?c) between $183.60 and $205.08?d) Which would be more unusual, a day on which the stock price closed
=+28. Stock prices. 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
=+d) Which would be more unusual, a day on which the pound was worth less than 1.126 euros or more than 1.298 euros?
=+probability that on a randomly selected day during this period, the pound was wortha) less than 1.19 euros?b) more than 1.233 euros?c) less than 1.104 euros?
=+27. Currency exchange rates. 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
=+26. Human resource testing, again. For the IQ test administered by human resources and discussed in Exercise 24, what cutoff value would separate thea) lowest 0.15% of all applicants?b) lowest
=+25. Mutual funds, again. 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
=+would have what probability of scoring in the following regions?a) 100 or belowb) Above 148c) Between 84 and 116d) Above 132
=+24. Human resource testing. 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
=+23. Mutual fund returns 2013. 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
=+For Exercises 23–30, use the 68–95–99.7 Rule to approximate the probabilities rather than using technology to find the values more precisely. Answers given for probabilities or percentages
=+b) What is the probability that the next sale will happen in the next 6 minutes?Chapter Exercises
=+a) If a sale just occurred, what it the expected waiting time until the next sale?
=+22. Suppose occurrences of sales on a small company’s website are well modeled by a Poisson model with l = 5>hour.
=+b) With this model, what would the probability be that a hard drive lasts 5 years or less?
=+a) What value of l should they use?
=+21. Lifetimes of electronic components can often be modeled by an exponential model. Suppose quality control engineers want to model the lifetime of a hard drive to have a mean lifetime of 3
=+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?
=+20. 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
=+c) Numbers above 9000 were only released for domestic use last year, so they went to newly constructed residences.What is the probability that a randomly selected number will be one of these?
=+b) The new business “incubator” was assigned the 200 numbers between 452-2500 and 452-2699, but these businesses don’t subscribe to digital TV. What is the probability that the randomly
=+a) What distribution would they use to model the selection?M07_SHAR8696_03_SE_C07.indd 263 14/07/14 7:31 AM 264 CHAPTER 7 The Normal and Other Continuous Distributions
=+19. 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
=+b) Do you think this is evidence that spinning a Belgian euro is unfair? Would you be willing to use it at the beginning of a sports event? Explain.Section 7.6
=+determine the probability of spinning a fair coin 250 times and getting at least 140 heads.
=+18. 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
=+b) Should the airline change the number of tickets they sell for this flight? Explain.
=+a) Use the Normal model to approximate the Binomial to determine the probability of at least 246 passengers showing up.
=+17. 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
=+b) The team’s best time so far this season was 3:19.48.(That’s 199.48 seconds.) What is the probability that they will beat that time in the next event?Section 7.5
=+a) What are the mean and standard deviation for the relay team’s total time in this event?
=+• The means and standard deviations of the times (in seconds) are as shown here.Swimmer Mean SD 1 (backstroke) 50.72 0.24 2 (breaststroke) 55.51 0.22 3 (butterfly) 49.43 0.25 4 (freestyle) 44.91
=+• The swimmers’ performances are independent.• Each swimmer’s times follow a Normal model.
=+16. In the 4 * 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
=+b) What is the probability they won’t have to change tires a third time (and use a fourth set of tires) before the end of a 500-mile race?
=+a) If the team plans to change tires twice during a 500-mile race, what is the expected value and standard deviation of miles remaining after two changes?
=+15. 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
=+14. 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.0.0 75.0 150.0 225.0 200
=+13. Speeds of cars were measured as they passed one point on a road to study whether traffic speed controls were needed. Here’s a histogram and normal probability plot of the measured speeds. Is
=+12. In a standard Normal model, what value(s) of z cut(s)off the region described? Don’t forget to draw a picturea) The lowest 20%b) The highest 15%c) The highest 20%d) The middle 50%Section 7.3
=+11. In a standard Normal model, what value(s) of z cut(s)off the region described? Don’t forget to draw a picture.a) The highest 20%b) The highest 75%c) The lowest 5%d) The middle 90%
=+10. What percent of a standard Normal model is found in each region? Draw a picture first.a) z 7 -2.05b) z 6 -0.33c) 1.2 6 z 6 1.8d) z 6 1.28
=+9. Assuming a standard Normal model, what is the probability for each of the following cases?. Be sure to draw a picture first.a) z 7 -1.5b) z 6 1.75c) -2 6 z 6 1.35d) z 7 0.35
=+e) About what percent of people should have IQ scores above 132?
=+d) About what percent of people should have IQ scores between 68 and 84?
=+c) About what percent of people should have IQ scores above 116?
=+b) In what interval would you expect the central 95% of IQ scores to be found?
=+a) Draw the model for these IQ scores. Clearly label it, showing what the 68–95–99.7 Rule predicts about the scores.
=+a mean of 100 and a standard deviation of 16.
=+8. Some IQ tests are standardized to a Normal model with
=+e) Describe the gas mileage of the worst 2.5% of all cars.
=+d) About what percent of cars should get between 31 and 37.2 mpg?
=+c) About what percent of autos should get more than 31 mpg?
=+b) In what interval would you expect the central 68% of autos to be found?
=+a) Draw the model for auto fuel economy. Clearly label it, showing what the 68–95–99.7 Rule predicts about miles per gallon.
=+7. 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
=+b) What do you need to assume about the heights of 2-year-olds to find your answer to part a?Section 7.2
=+a) Does this child fall into that group?
=+6. The pediatrician in Exercise 4 explains to the parents that the most extreme 5% of cases often require special treatment or attention.
=+b) What do you need to assume about test scores to find your answer in part a?
=+a) With your z-score of 2.20, did you make the cut?
=+5. 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.
=+4. After examining a child at his 2-year checkup, the boy’s pediatrician said that the z-score for his height relative to American 2-year-olds was -1.88. Write a sentence to explain to the
=+3. Your company’s Human Resources department administers a test of “Executive Aptitude.” They report test grades as z-scores, and you got a score of 2.20. What does this mean?
=+2. The first Statistics exam had a mean of 65 and a standard 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
=+On which exam did she do better compared with the other students?
=+1. 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
=+• Propose an ethical solution that considers the welfare of all stakeholders.
=+• What are the undesirable consequences?
=+• Identify the ethical dilemma in this scenario.
=+3. In the past week of 5 days of production, they’ve rejected 200 screens—an average of 40 per day. Should that raise concerns?
=+2. If they reject 40 screens today, is that a large enough number that they should be concerned that something may have gone wrong with the production line?
=+ What is the standard deviation?
=+1. How many screens do they expect to reject in a day’s production run of 500 screens?
=+What percentage of stereo systems take longer to pack than to box?
=+What is the probability that packing an order of two systems takes more than 20 minutes?
=+What does this plot say about the distribution of the CAPE10 scores?
=+d) What does this say about the accuracy of your prediction?Explain.

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