An insurance company found that 2.5% of male drivers between the ages of 18 to 2

Question

An insurance company found that 2.5% of male drivers between the ages of 18 to 25 are involved in serious accidents annually. To simplify the analysis, assume (artificially) the following: 1) every such accident costs the insurance company $50,000; 2) a driver can only have one of these accidents in a year; 3) the insurer charges $2,000 for a policy; 4) the accidents occur independently of each other.

Suppose that the company writes 1,000 such policies to a collection of drivers as described above. Describe the total payments from these policies by the random variable Y. What are the expected value and SD of Y?

Explanation / Answer

b) n=1000 x=40 p=.025 mean = np = 1000*.025 = 25 sd = sqrt(npq)= sqrt(1000*.025*(1-.025)) = 4.94

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