Question: The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days.

(a) One classical use of the normal distribution is inspired by a letter to Dear Abby in which a wife claimed to have given birth 308 days after a brief visit from her husband, who was serving in the Navy. Given this information, find the probability of a pregnancy lasting 308 days or longer. What does the result suggest?

(b) If we stipulate that a baby is premature if the length of pregnancy is in the lowest 4%, find the length that separates premature babies from those who are not premature. Premature babies often require special care, and this result could be helpful to hospital administration in planning for that care.