In processing a random sample of 200 auto insurance claims obtained from an insu

Question

In processing a random sample of 200 auto insurance claims obtained from an insurance company, the mean is $823 and the standard deviation is $78. Assume claims are normally distributed.

a. What is the probability that a claim submitted exceeds $885

b. What is the probability that a claim submitted will be less than $740 and

c. Management wants to focus on the claims representing the top 8% (in terms of $ amount of claims). Help find the $ amount for the claim that marks the limit for the top 8%.

Explanation / Answer

Given n=200, X~Normal(mean=823, s=78) --------------------------------------------------------------------------------------------------------------- a. What is the probability that a claim submitted exceeds $885 P(X>885) = P((X-mean)/s > (885-823)/78) =P(Z>0.79) =0.2147 (check standard normal table) --------------------------------------------------------------------------------------------------------------- b. What is the probability that a claim submitted will be less than $740 and P(X P(X P(Z (c-823)/78 =1.41 (check standard normal table) --> c=823 +1.41*78 = 932.98

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