A company that sells annuities must base the annual payout on the probability di

Question

A company that sells annuities must base the annual payout on the probability distribution of the length of life of the participants in the plan. Suppose the probability distribution of the lifetimes of the participants is approximately normally distributed with a mean of 68 years and a standard deviation of 3.5 years. What is the probability that plan recipients would live to receive payments beyond age 75? a) 0.9772 b) 0.5228 c) 0.4775 d) 0.0228 What probability that plan recipient die before they reach the standard retirement age of 65 (round to the nearest hundredths places)? a) 0.0635 b) 0.1949 c) 0.6951 d) 0.8051

Explanation / Answer

Mean = 68

Standard deviation = 3.5

8. P(plan recepients would live to receive payments beyond 75) = P(X>75)

= 1 - P(X < 75)

= 1 - P(Z < (75 - mean)/standard deviation)

= 1 - P(Z < (75 - 68)/3.5)

= 1 - P(Z < 2)

= 1 - 0.9772

= 0.0228 (option d)

9. P(plan recipient die before reaching 65) = P(X<65)

= P(Z < (65-68)/3.5)

= P(Z < -0.86)

= 0.1949 (option b)

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