Hypothesis Tests · Challenge problem

A test uses $\bar x$ with SE $1$ to decide between $\mu = 20$ ($H_0$) and $\mu = 23$ (the alternative), rejecting $H_0$ when $\bar x > c$. Choose $c$ so that the probability of a Type I error equals the probability of a Type II error (at $\mu = 23$). What is that common probability? Give your answer to four decimal places.