Confidence Intervals · Superchallenge problem

A new treatment is tried on 20 patients and none has a side effect. The ordinary interval $\hat p \pm z^*\sqrt{\hat p(1-\hat p)/n}$ collapses to the single point 0. Instead, collect every $p$ with $|\hat p - p| \le z^*\sqrt{p(1-p)/n}$, using $z^* = 2$. What is the UPPER end of this interval? Give a fraction.