I was working on a problem that was dealing with proportions and it asked the following:
If a population proportion is believed to be $0.6$, how many items must be sampled to ensure that the sampling distribution of $\hat{p}$ will be approximately normal? Assume that the size of the population is $N = 10,000$.
I know that the Normal condition for a sampling distribution is $np\geq 10$ and $n(1-p)\geq 10$. I got that the answer was $25$ with this reasoning. The answer key says that it is 42. I am not sure what am I missing here. I computed $42\times 0.6=25.2$ but don't know if that is actually something I am supposed to use. Any help is appreciated.
Thank you.
I believe it should be that $np>10$ and $np(1-p)>10$. This would give that $n>41 \frac{2}{3}$ which is probably what you want.