5. Suppose $X \sim \operatorname{Binomial}(n, p)$ and let $\hat{p}_{n}=X / n$. Show that $\sqrt{n}\left(\hat{p}_{n}-p ight) / \sqrt{\hat{p}_{n}\left(1-\hat{p}_{n} ight)}$ converges in distribution to a standard normal distribution. SP. AS373