A particularly useful example of the Central Limit Theorem is when
we are sampling from a 0-1 population. In this case, the number
of 1's observed has the binomial distribution which is difficult
to make calculations from. But notice that 
for the
sample is in fact the sample proportion p and the Central
Limit Theorem says that is approximately normal with
mean equal to the mean of the 0-1 population (also known as 
, the
proportion of 1's in the population) and variance 
.
See the ``Z, t, Chi-square, F'' concept lab.