The lengths of pregnancies are normally distributed with a mean of 267 days and a standard deviation of 15 days. (a) Find the probability that an individual woman has a pregnancy shorter than 259...

The lengths of pregnancies are normally distributed with a mean of 267 days and a standard
deviation of 15 days.
(a) Find the probability that an individual woman has a pregnancy shorter than 259 days.
(b) If 36 women are randomly selected, find the probability that they have a mean preg-
nancy shorter than 259 days.
(c) There should be a difference in your method for the previous two questions. Explain
what you did differently for each problem and explain WHY your answers are different.
(d) Find the probability that an individual woman has a pregnancy longer than 295 days.
(e) Find the probability that an individual woman has a pregnancy between 259 and 295
days.
(f) What is the cutoff number of days for a pregnancy for the top 15% of women?
(g) What is the cutoff number of days for a pregnancy for the bottom 25% of women?