C.I. for Bin(n,p) using pivots.

#1
Problem: Let $X$ be $Bin(n,p)$ and $\hat p = X/n$, and $$Z=\frac{\hat p - p}{\sqrt{p(1-p)/n}}$$ We see that $Z$ is asymptotically $N(0,1)$. Find a $1-\alpha$ confidence interval for $p$. Note that this is very different from the regular $$\frac{\hat p - p}{\sqrt{\hat p(1-\hat p)/n}}$$

Attempt: I think I should use a Wald (or perhaps a Score) interval to solve this. I have found this document that describes how it's done, but I don't know if it's the right approach. Furthermore, it's an undergrad course in probability so we don't know very much.

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[1]: http://i.stack.imgur.com/WrTNe.png
[2]: http://i.stack.imgur.com/d1blo.png