sampling distribution of sample mean!?

Question

A population has a mean of 200 and a standard deviation of 50. A simple random sample of size 100 will be taken and the sample mean x ̅ will be used to estimate the population mean.

Show the sampling distribution of x ̅.

How do I show whether the sampling distributing of the sample mean is normal or not normal?!?

Answer 1

The distribution for x-bar won't be normal exactly, unless the population has a normal distribution. But a sample size of 100 is large enough to allow you to invoke the central limit theorem and conclude that the distribution of the sample mean is "approximately normal".

Answer 2

Twice.