Hypothesis Tests · Challenge problem

To test $H_0\!: p = 0.5$ against $H_a\!: p > 0.5$ at $\alpha = 0.05$, a pollster rejects $H_0$ when $\hat p > 0.5 + 1.645\sqrt{0.25/n}$. Using the normal approximation, where $\hat p$ has standard deviation $\sqrt{p(1-p)/n}$ under the true $p$, what is the smallest sample size $n$ that gives power at least $0.80$ when in fact $p = 0.6$? (The $z$ value with upper tail area $0.20$ is $0.8416$.)