calculating confidence of an APS score

I don't actually think this can be correctly modelled by a unimodal distribution - you will be adding thin gaussians to fat gaussians, making horrible bumps which don't like to be approximated by a single gaussian mean+stdev. I almost wonder if some sort of [ http://en.wikipedia.org/wiki/Monte_Carlo_method Monte-Carlo] solution wouldn't be most accurate in this instance - at least the math would be easy to understand.