A Company that sells annuities must base the annual payout on the probability distribution of the length

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 in the plan is approximately a normal distribution with = 68 years and = 3.5 years.

1. What proportion of the plan participants would receive payments beyond age 75?

2. What proportion of plan participants die before they reach the standard retirement age of 65 years?

3. Find the age at which payments have ceased for approximately 86% of the plan participants.

Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...