I want to show that this function:

(P^ - p) / (root)((p(1-p))/n)

will approximate the standard normal distribution. Here P^ is an unbiased estimator for p, and p is the probability for an event. n is the number of trials.

The first thing I notice is that this formula looks very similiar to the formula used in the central limit theorem, so I am guessing that there is a way to manipulate this one into that one. My textbook doesn't explain or proove these things, so any help to make me understand this will be very appreciated!