Stat 11 Homework 3 Due 5/12/04 1. Of Colossal Conglomerate's 16,000 clients, 3,200 own their own business, 1,600 are "gold class" customers, and 800 own their own business and are also "gold class" customers. What is the probability that a randomly chosen client who owns his or her own business is a "gold class" customer? 2. You have invested in Home-Clone Inc. stocks, as you suspect that the company's "Clone-a-Sibling" kit will shortly be approved by the FDA. There is an 80% chance that FDA approval will be given, and a 95% chance that the value of the stock you hold will double if FDA approval is given. What is the probability that the FDA will approve the product and the value of the stock you hold will double? 3. In a certain population, 30% of the persons have accounting training and 8% have a computer training. Moreover, 12% of the persons who have accounting training have computer training. A. What percent of the population that accounting training has computer training? B. What percent of the population with computer training also have accounting training? C. Are computer training and accounting training independent? D. Are computer training and accounting training mutually exclusive? 4. Gondor Stewards, an auditing firm, has been hired to audit the books for the Rivendell Marketing Research. Anduin Took, Gondor Stewards top auditor, has been given this assignment. Rivendell, which has twenty-three clients of their own, only wants a quick overview rather than a complete audit. Because of this, Ms. Took decides to only audit the accounts for five randomly selected Rivendell clients. The results of her audit are provided below: Rivendell Client Number of Correct Entries Number of Incorrect Entries Misty Mountain Furniture Makers 1219 38 Greenleaf’s Appliance Production 2436 112 Rose Cotton’s Maid Service 844 11 Fangorn Dry Cleaners 1856 39 Mordor Kennels 564 17 Before we start answering the proceeding questions, let’s agree on some notation for particular events in our data. We’ll let A = Correct Entry (so A’ = Incorrect Entry), B1 = Misty Mountain Furniture Makers, B2 = Greenleaf’s Appliance Production, B3 = Rose Cotton’s Maid Service, B4 = Fangorn Dry Cleaners, and B5 = Mordor Kennels. A. Using the data collected by Ms. Took, what would you estimate to be the probability of an incorrect entry? B. Ms. Took has selected Mordor Kennels at random. What would you estimate to be the conditional probability of an incorrect entry in their books?Stat 11 Homework 3 Due 5/12/04 C. What would you estimate to be the probability that an entry in Rivendell’s books is drawn from a manufacturing organization (Misty Mountain Furniture Makers or Greenleaf’s Appliance Production)? D. What would you estimate to be the probability that an entry in Rivendell’s books is drawn from a service organization (Rose Cotton’s Maid Service or Fangorn Dry Cleaners or Mordor Kennels)? E. What would you estimate to be the probability that an incorrect entry found in the books is from a service organization? F. Restructure the table so that it is simply manufacturing & service organization versus correct and incorrect (we don’t care about the names any more, just the type). Do the type of industry (service vs. manufacturing) and the status of an entry in the books (correct or incorrect) appear to be independent? Please explain. 5. In a certain zip code it is known that 80% of the adult women shop online. If 12 women from this zip code are selected at random, what is the probability that 9 of them will shop online? Please assume independence. 6. There are 27 students in a discussion section in Statistics. Let x be the random variable which gives the age (rounded to the nearest year) of a randomly chosen student on the day of the final exam. (i) Is X a discrete or a continuous random variable ? Is x a finite random variable ? Explain. (ii) Assume that on the day of the final exam, 3 of the students are 17 years old, 5 are 18 years old, 10 are 19 years old, 6 are 20 years old and 3 are 21 years old. Answer the following questions (you may give your answers as fractions): • The p.d.f. f(x) has f(x) =f(19) • P( x < 22) • P(17 < x < 22) • The c.d.f. F(x) has F(x)=F(20) (iii) Based on the information given in (ii), find the expected value of x and the standard deviation of x. Show all your work. 7. You are a loan officer and have to decide whether you should foreclose on one of your clients. You are given the following information: the full value of this person's loan is $300,000; the foreclosure value is $150,000 (i.e. a loss of $150,000 to your bank) and the default value is $50,000 (i.e. a loss of $250,000 to your bank). You looked at past bank records and you estimated that the probability of your bank getting the full value following a “workout” with the client is 0.35 and the probability of default following a “workout” is .40. Assuming that the “break-even” value is $150,000 please decide whether you recommend workout or foreclosure for this loan. Justify your recommendation