Question

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?

Answer 1

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.