states that the sample mean will be approximately normally distributed for large sample sizes, regardless of the distribution from which we are sampling (normal or not)
we can often use the well-developed statistical inference procedures that are based on a normal distribution, given we have a large sample size
very rough guideline
for , the sample mean can be considered approximately normally distributed
sometimes we cant know the distribution of X, but Z using will have the normal distribution (so we can easily calculate it)