Yet another thought on using the normal approximation to find a confidence for p when we technically don't know the standard deviation (since we need to know p to know the standard deviation):
Consider the variance for one binomial trial: p(1-p). Regardless of the true value of p, we do know that p(1-p)<=1/4. Hence if we replace p(1-p) with 1/4 we will error by possibly making the standard deviation (of the number of trials or of the proportion) too big. That will have the effect of making our confidence intervals larger than they might have to be. I.E. we will error on the side of caution.
-- Doug Kuhlmann (508)-749-4242 Phillips Academy email@example.com Andover, MA 01810 firstname.lastname@example.org