Normal distribution is deeply inapproprite for time estimation because it yields the same probability for 3x the estimated time than for the negative amount(!)

Normal distribution is deeply inapproprite for time estimation because it yields the same probability for 3x the estimated time than for the negative amount(!) of the estimated time. Your second point rings closer to what we should be doing instead. We should put more effort into analysis and refinement. In my experience, estimation meetings where all tasks got estimated were almost useless in the end; and the most valuable meetings where when we didn't finish to estimate, but instead gained a deeper understanding of the requirements and of the domain.