Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean mu equals 280 days and standard deviation sigma equals 15 days. (a) what is the probability that a randomly selected pregnancy lasts less than 275 days?

First, find the z-score:

z = (value - mean) / sdev

= (275 - 280) / 15

= - 0.33

In order to use a standard normal table, we need a positive z-score:

P (z < - 0.33) = 1 - P (z < 0.33)

Looking at the table, we find P (z < 0.33) = 0.6293

Therefore:

P (z < - 0.33) = 1 - 0.6293 = 0.3707

Hence, you have a probability of about 37% that a randomly selected pregnancy lasts less than 275 days.