Section 9 Central Limit Theorem

The Central Limit Theorem states that for large samples, the sample mean has an approximate normal distribution whatever the distribution of the original variable.

In many situations, irrespective of the the distribution of \(\large X\):

\[\Huge If \hspace{6mm} n > 30\]

\[\Huge Then \hspace{6mm} \bar{x} \sim Normal(\mu, \frac{\sigma^2}{n})\]

Hence it is possible to make statements about the sample mean even if the exact distribution of values in the original population is unknown.