Assume that is a bivariate normal with and and I want to find . Is it true that )? Then I can just integrate that from to .5. Is this correct?
You don't, it's intractable (when I said "looks good" I didn't think you would try to integrate analytically) . Standardize X and use a Z-Table or software. The question is essentially asking the probability of X being one standard deviation below the mean, or more; should be, what, 16% or so?