Probability theory and project planning [closed]

Question

I'm managing a project that has to be estimated, according to rough requirements and specifications. Because of that, the estimations on the specific features and tasks are set of discrete values, instead of just one discrete value (for example, between 10 and 20, instead of exactly 17).

I'm curious, if I want to get an idea of the approximate probability to finish some task within the lowest estimate, how should I approach this? Please, for the sake of the discussion, disregard factors like my estimation skills, used platform, etc.

I was thinking about using Poisson distribution, with λ = (low + high) / 2, assuming that the probability for each of the proposed values abides to the law of rare events / normal distribution. This doesn't account for the fact that going out of my estimation limits is more unlikely than likely, but still...

What do you think about that, and which approach would you choose for such experiment?