Sammy, I still don't think I'm looking at it correctly. It doesn't seem solvable with the data provided.
Heuristics tells me about .260-.265, as the pitcher is going to need a bluff% of 10 to keep the batter on his toes, but the batter will be optimistic and look for more curveballs.
But I still need to nail down one more variable to come up with a single answer.