Question

Your company sells life insurance. You charge a 55 year old man $60 for a one year, $100,000 policy. If he dies over the course of the next year you pay out $100,000. If he lives, you keep the $60. Based on historical data (relative frequency approximation) the average 55 year old man has a 0.9998 probability of living another year.

(a) What is your expected profit on this policy?

(b) What is an accurate interpretation of this value?

It represents the loss on every policy sold.

It represents the profit on every policy sold.

It represents the average profit per policy sold that you would expect if you sold a lot of these policies.

It is meaningless because the insurance company never makes this amount on a policy.

Answer 1

P(living next year) = 0.9998

Profit = $60

Loss = 100000-60 = $99940

a) Expected profit = 0.9998 * 60 - (1 - 0.9998) * 99940 = $40

b) Option-C) It represents the average profit per policy sold that you would expect if you sold a lot of these policies.