A clinical trial evaluates a drug's success. The researcher computes an Agresti-Coull interval for the probability $p$ with $x$ successes in $n$ trials using $\tilde{p} = \frac{x+2}{n+4}$ and $\tilde{n} = n+4$. Why is this interval preferred over the standard Wald interval $\hat{p} \pm z \sqrt{\hat{p}(1-\hat{p})/n}$?