Why not go for the 1st/2nd order taylor series approximation aka basic kinematics approximation of your target's motion in the future few seconds?
But anyhow, perhaps by bell curve you mean randomly guessing firing solutions in a test environment then constructing a bell curve to help select (and interpolate?) a relevant firing solutiont from a table of known firing solutions at game time?
But a few more details would be nice.
-q