What is the sampling distribution of p hat?

The sampling distribution of (\hat{p}) (the sample proportion) describes the distribution of sample proportions obtained from repeated random samples of a given size from a population. It is approximately normal when the sample size is large enough, typically when both (np) and (n(1-p)) are greater than 5, where (p) is the population proportion and (n) is the sample size. The mean of this distribution is equal to the population proportion (p), and the standard deviation (standard error) is given by (\sqrt{\frac{p(1-p)}{n}}).