The Central Limit Theorem states (Page 274) that

The sampling distribution of the mean of a random sample drawn from any population is approximately normal for a sufficiently large sample size. The larger the sample size, the more closely the sampling distribution of will resemble a normal distribution.. For the sampling distribution of the sample mean, ,

1. 

2. 

   (called the standard error of the mean or SE mean on Minitab).

3. If X is normal, then is normal (exactly). If X is nonnormal, is approximately normal for sufficiently large sample sizes. The definition of ``sufficiently large'' depends on the extent of nonnormality of X.