ADMN 420 - Homework no: 03 8% of all claims filed with an insurance company are fraudulent. The manager of the claims division suspects that the percentage of fraudulent claims may have decreased after the recent implementation of new customer filing procedures that discourage fraud. To test this theory, a random sample of 120 recently filed claims was selected. After careful investigation of each of these 120 claims, only 2 are found to be fraudulent. Q1. Assume that the true fraudulent claim rate has remained at 8%. Compute the probability of 2 or fewer fraudulent claims in a random sample of 120 claims. a) 0.003 b) 0.10 c) 0.11 d) 0.22 Q2. Based on your answer in part (a), what do you conclude about the possible decrease in the fraudulent claim percentage? a) There is a decrease b) There is an increase c) Stayed the same d) Not enough information to answer the question Logging trucks have a particular problem with tire failures due to blowouts, cuts and large punctures; these trucks are driven fast over very rough, temporary roads. Assume that such failures occur according to a Poisson distribution at a mean rate of 4 per 10,000 miles. Q3. If a truck drives 1000 miles in a given week, what is the probability that it does not have any tire failures? a) 0.673 b) 0.723 c) 0.589 d) 0.111 Q4. What is the probability that it has at least two failures? a) 0.673 b) 0.061 c) 0.589 d) 0.01 Q5. What is the expected values of the number of tire failures per 1000 miles drive? a) 0.4 b) 0.8 c) 0.632 d) 4 Q6. What is the standard deviation of the number of tire failures per 1000 miles drive? a) 0.4 b) 6 c) 0.632 d) 40 A telephone-sales firm is considering purchasing a machine that randomly selects and automatically dials telephone numbers. The firm would be using the machine to call residences during the evening; calls to business phones would be wasted. The manufacturer of the machine claims that its programming reduces the business-phone rate to 15%. As a test, 100 phone numbers are to be selected at random form a very large set of possible numbers. Q7. Find the probability that at least 24 of the numbers belong to business phones. a) 0.012 b) 0.15 c) 0.015 d) 0.12 Q8. Find the expected value of the number of business-phone numbers. a) 15 b) 24 c) 100 d) 12 Q9. Find the variance of the number of business-phone numbers. a) 12.75 b) 225 c) 5 d) 50 Q10. You pay close attention to quality in your production facilities, but the logic analyzers you make are so complex that there are still some failures. In fact, based on past experience, about 97% of the finished products are in good working order. Today you will have to ship 17 of these machines. The question is: How many should you schedule for production to be reasonably certain that 17 working logic analyzers will be shipped (so that 90% of the produced are in working order)? Hint: Use excel to answer this question for trial and error. a) 19 b) 10 c) 17 d) 16 Because your firm's quality is so high, you expect only 1.3 of your products to be returned, on average, each day for warranty repairs. What are the chances that Q11. No products will be returned tomorrow? a) 0.27 b) 0.35 c) 0.23 d) 0.09 Q12. That one will be returned? a) 0.27 b) 0.35 c) 0.23 d) 0.09 Q13. How about two? a) 0.27 b) 0.35 c) 0.23 d) 0.09 Q14. How about three? a) 0.27 b) 0.35 c) 0.23 d) 0.09