Question

A company that sells annuities must face the annual payout on the probability distribution of life of participants in the plan. Suppose probabilities distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 3.5 years. If a participant was randomly selected what is the probability that participant would die between the age of 70 and 75?

Answer 1

Mean = 68

S.D. = 3.5

Z score at X = 70

Z = (X - μ) / σ
Z = (70 - 68) / 3.5
Z = 0.571

Z Score at X = 75

Z= (X - μ) / σ
Z = (75 - 68) / 3.5
Z = 2

P( 70< X < 75)= P(0.571 < Z < 2)

= P(Z < 2)- P( 0.571 < Z) = 0.2611