Central Limit Theorem : Application in Bernoulli Distribution

Question

I am currently facing with the central limit theorem aplication. The goal was to find other distribution that can be use to calculate a distribution.
The problem was :
suppose we have random sample $X_{1},X_{2},...,X_{n}$ that are collected from a population with Bernouli {$X$~$Be(p)$}. Find an another distribution that relate to : $\frac{\bar{X}-p}{\sqrt{\frac{\bar{X}(1-\bar{X})}{n}}}$.
I am a little bit confused, because it is just a bit different than $\frac{\bar{X}-p}{\sqrt{\frac{p(1-p)}{n}}}$ which can be approximate with standard normal distribution $N(0,1)$. since $p$ and ${p(1-p)}$ is a mean and variance of Bernoulli distribution $p$ and $p(1-p)$, which is a mean and variance of the population (so that we can apply Central Limit Theorem). Can you help me in this problem?