So a Poisson distribution is for count data, not continuous like time. A gamma distribution is a continuous distribution that have the shape you want. But, this

So a Poisson distribution is for count data, not continuous like time. A gamma distribution is a continuous distribution that have the shape you want. But, this approach should involve getting data and plotting it to see empirically what sort of distribution it might have. I’m also unclear how the dependency you mention is going to come in. That said I agree with you in general that some statistical reasoning should be brought to this problem. Maybe just showing people the way variances are additive and the impact that has on the overall variance of a project made of many small projects. You could pick a plausible gamma distribution for individual task duration and play around with seeing what the sum of a number of IID gammas looks like —- the sum is a gamma distribution also; see wikipedia but the formula.