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

(a) Find the probability that the length of a pregnancy is between 268 days or shorter.

(b) Find the probability of a pregnancy lasting 250 and 310 days.

(c) One 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 of longer. What does this result suggest?

(d) 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 administrations in planning for that care.