The lengths of pregnancies in number of days are normally distributed with a mean of

The lengths of pregnancies in number of days are normally distributed with a mean of 268 days and a standard deviation of 15 days. Answer the following questions and show your work.

a. If a pregnancy length is randomly taken from this distribution, what is the probability that the length of that pregnancy is less than 260 days?

b. If a sample of 25 pregnancies is taken from this distribution, what is the probability that their mean will be less than 260 days?

c. Explain why these two answers (from a and b) are different.