The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days.
a. If one pregnant female is randomly selected, find the probability that her length of pregnancy is less than 260 days.
b. If 25 randomly selected females are put on a special diet just before they become pregnant, find the probability that their lengths of pregnancy have a mean that is less than 260 days (assuming that the diet has no effect).
c. If the 25 females do have a mean of less than 260 days, should the medical supervisors be concerned?