I wasn’t using a normal distribution in my original formulation, though: the mean of the picture in my head was around 1 in a million with a longer tail to the right (towards 100%) and a shorter tail to the left (towards 0%) (on a log scale?). It could be that I was doing something stupid by making one tail longer than the other?
It would only be suspicious if your resulting probability were a sum of very many independent, similarly probable alternatives (such sums do look normal even if the individual alternatives aren’t).
I wasn’t using a normal distribution in my original formulation, though: the mean of the picture in my head was around 1 in a million with a longer tail to the right (towards 100%) and a shorter tail to the left (towards 0%) (on a log scale?). It could be that I was doing something stupid by making one tail longer than the other?
It would only be suspicious if your resulting probability were a sum of very many independent, similarly probable alternatives (such sums do look normal even if the individual alternatives aren’t).