Probability question help

Question

A company that sells annuities must base the annual payout on the distribution of the length of life of the participants in the plan. Suppose the distribution of male participants' lifetimes is normally distributed with a mean of 68 years and a standard deviation of 5 years. Let the random variable X represent the lifetime of a male participant. What is the probability that a male participant would die between 64 and 65 years old?

Answer 1

$$X \sim N(68,5^2)$$ Now, the probability that the male participant would die between 64 and 65 years is $$P(64<X<65)$$ $$=P(X<65) - P(X<64)$$ $$=P(z<\frac{65-68}{5} ) - P(z<\frac{64-68}{5}).$$

Compute the probability looking at the normal distribution table.