Hypothesis Tests · Superchallenge problem

A one-sided $z$ test of $H_0\!: \mu = \mu_0$ against $H_a\!: \mu > \mu_0$ has p-value $1 - \Phi(z)$. Suppose the truth is $H_a$ with an effect of exactly 2 standard errors, so $z = 2 + Z$ with $Z$ standard normal. What is the EXPECTED p-value? Round to three decimal places.