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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
=+c) What’s the standard deviation of the net profit?
=+b) What’s the mean of the net profit?
=+a) Define random variables and use them to express the shop’s net profit.
=+35. Skate board sale. A sports shop plans to offer 2 specially priced skate board models at a sidewalk sale. The basic model will return a profit of $120 and the sports model$150. Past experience indicates that sales of the basic model will have a mean of 5.4 skate boards with a standard
=+c) If gamblers play this machine 1000 times in a day, what are the mean and standard deviation of the casino’s profit?
=+b) If a gambler plays 5 times, what are the mean and standard deviation of the casino’s profit?
=+a) Why is the standard deviation so large?
=+34. Casino. 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.
=+d) At the end of a day, a worker comments “Boy, I’m tired.Today was sure unusually busy!” How many repair calls would justify such an observation.
=+c) Use the mean and standard deviation to describe what a typical 8-hour day will be like.
=+b) What assumption did you make about the repair calls?
=+a) Find the mean and standard deviation of the number of repair calls they should expect in a day.
=+33. Repair calls. Suppose that the appliance shop in Exercise 23 plans an 8-hour day.
=+d) What is the standard deviation of the number of defective pixels in the next 100 screens?
=+c) What is the expected number of defective pixels in the next 100 screens?
=+b) What is the standard deviation of the number of defective pixels per screen?
=+a) What is the expected number of defective pixels per screen?
=+32. Defective pixels. 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:X = # of Defective Pixels 0 1 2 3 4 or more P1X = x2 0.95 0.04 0.008 0.002 0
=+31. Commuting, part 2. 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?
=+c) Is it necessary to assume the blocks are independent?Why?
=+a) How many repairs after the semester does he expect to get?b) What’s the standard deviation?
=+30. Dormitory accommodation. The housing manager of dormitory accommodation for exchange students believes that the mean number of dormitories in need for some form of repair after each semester is 0.6 per block of 20 dormitories on the campus, with a standard deviation of 0.5. He is
=+d) What’s the standard deviation?
=+c) What’s the expected number of good batteries?
=+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 probability model for the number of good
=+29. Battery recall. A company has discovered that a recent
=+e) Find the expected value and standard deviation of X.
=+d) Let X be the number of contracts you get. Find the probability model for X.
=+b) Find the probability you get both contracts.c) Find the probability you get neither contract.
=+a) Are the outcomes of the two contract bids independent?Explain.
=+28. Contracts. 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.
=+e) What are the expected value and standard deviation of X?
=+d) Let random variable X be the number of tournaments they win. Find the probability model for X.
=+c) What’s the probability they win both tournaments?
=+b) What’s the probability that they lose both tournaments?
=+a) According to their estimates, are the two tournaments independent? Explain your answer.
=+27. Cricket tournament. A cricket goods shop was asked to sponsor the local team in two tournaments. They claim the probability that the team will win the first tournament is 0.4. If the team wins the first tournament, they estimate the probability of also winning the second is 0.6. They guess
=+b) What is the standard deviation?
=+a) Find the expected number of appearance defects in a new car.
=+26. Defects. 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.
=+b) What’s the standard deviation?
=+a) How many red lights should she expect to hit each day?
=+25. Commuting to work. 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:X = # of Red 0 1 2 3 4 5 p1X =
=+b) Find the standard deviation for the profit.
=+a) What’s the expected profit?
=+24. Software company. 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.
=+b) What is the standard deviation?
=+a) How many calls should the shop expect per hour?
=+number of repair calls that an appliance repair shop may receive during an hour.Repair Calls 0 1 2 3 Probability 0.1 0.3 0.4 0.2
=+23. Repairs. The probability model below describes the
=+b) Is the random variable discrete or continuous?
=+a) What are the possible values of this random variable?
=+22. New website, part 2. For the website described in Exercise 21, let Y = the total time (in minutes) that a customer spends during a visit to the website.
=+b) Is the random variable discrete or continuous?
=+a) Assuming that there are n different pages in total on your website, what are the possible values that this random variable may take on?
=+21. New website. You have just launched the website for your company that sells nutritional products online. Suppose X = the number of different pages that a customer hits during a visit to the website.
=+20. 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?Chapter Exercises
=+b) What is the probability that she finds at least one?
=+a) What is the probability that she finds no button flaws?
=+19. 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:
=+18. As in Exercise 17, you are phoning local businesses.You call three firms. What is the probability that all three are owned by women?
=+you find one owned by a woman. What probability model should you use? (Specify the parameters as well.)
=+17. 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
=+c) Do you think a uniform distribution might be appropriate as a model for this random variable? Explain briefly.M06_SHAR8696_03_SE_C06.indd 231 14/07/14 7:26 AM 232 CHAPTER 6 Random Variables and Probability Models
=+b) Is the random variable discrete or continuous?
=+16. Through the career services office, you have arranged preliminary interviews at four companies for summer jobs.Each company will either ask you to come to their site for a follow-up interview or not. Let X be the random variable equal to the total number of follow-up interviews that you might
=+15. At many airports, a traveler entering the U.S. is sent randomly to one of several stations where his passport and visa are checked. If each of the 6 stations is equally likely, can the probabilities of which station a traveler will be sent be modeled with a Uniform model?
=+car should be stopped for inspection. If the chance of any vehicle to be stopped for inspection is 15%, can we use a Bernoulli model to model if your car will be stopped for inspection? Check all of the conditions.Section 6.5
=+14. At a border entry point between two different states, a computerized system is used to randomly check whether a
=+d) A study (softwaresecure.typepad.com/multiple_ choice/2007/05/cheat_cheat_nev.html) found that 56% of M.B.A. students admit to cheating. A business school dean surveys all the students in the graduating class and gets responses that admit to cheating from 250 of 481 students.
=+What is the probability they choose all women?
=+c) A committee consisting of 11 men and 8 women selects a delegation of 4 to attend a professional meeting at random.
=+b) We record the distribution of home states of customers visiting our website.
=+a) You are rolling 5 dice and need to get at least two 6s to win the game.
=+13. Which of these situations fit the conditions for using Bernoulli trials? Explain.
=+12. A shipping company delivers certain types of computer sets to local and international clients. From previous data, it is noted that 2% of its deliveries will break during shipment. If the company ships two computer sets separately to undisclosed address, find the probability that both
=+d) What assumption must you make in part c?
=+11. A broker has calculated the expected values of two different financial instruments X and Y. Suppose that E1X2 = +100, E1Y2 = +90, SD1X2 = +12, and SD1Y2= +8. Find each of the following.a) E1X + 102 and SD1X + 102b) E15Y2 and SD15Y2c) E1X + Y2 and SD1X + Y2
=+10. 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) 0.5Yc) X + Yd) X - Y Mean SD X 80 12 Y 12 3
=+9. 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 Mean SD X 10 2 Y 20 5
=+b) Find the standard deviation of the type of down payment potential customers will need.Section 6.3
=+a) Find the expected value of the type of down payment potential customers will need.
=+8. A motor home sales department has created three plans for purchasing a new or used motor home for leisure to increase potential sales of its fleet. They estimate that 20%will choose plan 1, which includes no down payment with 10 years finance option; 40% will choose plan 2, which includes a
=+b) Find the standard deviation of the service charge.
=+a) Find the expected value of the service charge.
=+7. 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 $20 finance charge; and 20% use the third plan, which has a $30 finance charge.
=+6. Find the standard deviation of the day trader’s option value in Exercise 4.
=+5. Find the standard deviation of the book purchases in Exercise 3.
=+b) What do you think of this option?Section 6.2
=+a) What is her expected value of the option’s profit?
=+4. 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,
=+3. Suppose that the probabilities of a customer purchasing 0, 1, or 2 books at a book store are 0.5, 0.3, and 0.2, respectively. What is the expected number of books a customer will purchase?Exercises M06_SHAR8696_03_SE_C06.indd 230 14/07/14 7:26 AM Exercises 231
=+b) What are the possible values it can take on?
=+b) What are the possible values it can take on?
=+1. A company’s employee database includes data on whether or not the employee includes a dependent child in his or her health insurance.a) Is this variable discrete or continuous?
=+• Propose an ethical solution that considers the welfare of all stakeholders.
=+• What are the undesirable consequences?
=+• Identify the ethical dilemma in this scenario.
=+6. What assumptions are you making to answer these questions?
=+5. If she calls 10 investors, what is the probability that exactly 2 of them will be interested?
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