6.44)

An insurance adjuster has been asked to undertake a survey of automobile collision claims. He plans to take a random sample of 200 claims from a computerized record of 8,200 claims. He operates under the premise that exactly 1% of the computerized record consists of blatantly fraudulent claims. He wants to know the probability of getting at most three of these blatantly fraudulent claims in his sample.

(a) Identify the values of a, b and n for this hypergeometric situation.

(b) The binomial approximation is appropriate here. Identify the values of n and p for the binomial approximation.

(c) Use the Poisson approximation to the binomial distribution and determine the probability that the sample will have at most three blatantly fraudulent claims.

(d) Suppose that the adjuster decides to change the 1% premise to 1.5%. For this revised premise, use the same approximation as in part (c) to determine the probability that the sample will have at most three blatantly fraudulent claims.