Answer to Question #10442 in Statistics and Probability for John

Question

A population has a mean of 20 and a standard deviation of 5.4. A simple random sample of size 35 will be taken and the sample mean will be used to estimate the population mean. Specify the sampling distribution of X bar. (X with a bar above it)

Answer 1

To solve the problem, ones need to know the precise distribution of the element of the sample. I believe, that they have N(20, 5,4^2), hence due to the properties of independent gaussian r.v. X ~ N(20, 5,4^2/30).