The lengths of pregnancies are normally distributed with a mean of 264 days and a standard deviation of 15 days. if 36 women are randomly selected, find the probability that they have a mean pregnancy between 264 days and 266 days.

Given that a sample of 36 women is selected, the probability that the mean is between 264 days and 266 days will be found as follows:

the std deviation of the sample will be:

σ/√n

plugging the values we obtain:

15/√36

=15/6

=2.5

hence the z-score when x=264 will be:

z = (264-264) / 2.5

z=0

thus:

P (x<264) = P (z<0) = 0.5

the z-score when x=266 will be:

z = (266-264) / 2.5

z=0.8

hence

P (x<266) = P (z<0.8) = 0.7881

thus

P (264
=0.7881-0.5

=0.2881

Answer: 0.2881