Question

The length of pregnancies are normally distributed with a mean of 260 days and standard deviation of 12 days. If 30 women are randomly selected, find the probability that lengths of pregnancy have a mean that is less than 255 days.

Answer 1

$P(\bar X<255)=P(Z<\frac{255-260}{\frac{12}{\sqrt{30}}})=P(Z<-2.28)=0.0113.$