A life insurance salesman operates on the premise that the probability that a ma

Question

A life insurance salesman operates on the premise that the probability that a man reaching his sixtieth birthday will not live to his sixty-first birthday is 0.06. On visiting a holiday resort for seniors, he sells 9 policies to men approaching their sixtieth birthdays. Each policy comes into effect on the birthday of the insured, and pays a fixed sum on death. All 9 policies can be assumed to be mutually independent. Provide answers to the following to 3 decimal places. What is the expected number of policies that will pay out before the insured parties have reached age 61? 0.06.9 What is the variance of the number of policies that will pay out before the insured parties have reached age 61? 0.06 (1-0.0 What is the probability that at least two policies will pay out before the insured parties have reached age 61? 0.329

Explanation / Answer

Solution:

Part a)

This is Binomial with n = 9 and p = 0.06

mean = np = 9(0.06) = 0.54

Part b)

variance = npq = 9(0.06)(1-0.06) = 0.5076

Part c)

P(X 2) = 1 - P(0) - P(1)

= 1 - 9C0(0.06^0)(0.94^9) + 9C1(0.06^1)(0.94^8)

= 1- 1(0.572) + 9(0.036)

= 1 - 0.896 = 0.104

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