Central Limit Theorem for Proportions
When you take samples from a population and compute a proportion from each one, you can consider the distribution of those proportions. This is called the sampling distribution for the population proportion.
The Central Limit Theorem tells us that the sampling distribution for the population proportion is with the as its .
The mean of the sampling distribution is given by .
If the samples have size , then the standard deviation of the sampling distribution is given by .