Question

Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean mu equals 205 days and standard deviation sigma equals 17 days. Suppose a random sample of 17 pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies.

The sampling distribution of x is

Answer 1

Let X denote length of the pregnancy. Here, X N(u= 205, a = 17) Number of pregnancies taken into the sample, n17 Let the sample mean be, X Since parent population normal, the sampling distribution of sample mean is also normal with mean and standard deviations are: 17 4.1231 Vn The sampling distribution of X is normal with mean 205 and standard deviation 4.1231