Trade-Offs

Non-normality Approximated by Normality

We consider the time estimates normally distributed random variables. However, these can take any value - negative and positive alike, albeit with often small probabilities, while time taken is nonnegative (at least by today's mainstream physics). So this is not 100% realistic - but simplifies the calculations greatly. And if you aren't expecting to work with 50%+ 1SD error margins, which is not a small uncertainty), then it means the possible values from our model are at least with a 97.5% probability are nonnegative (the ±2SD interval, see this chart). Had the margin shrunk to 25%, this irregularity became negligible: depending on the purpose, it might not be that bad a match.

Independence of Estimates

Then we also consider the variables independent. Well, chances of this are pretty slim to be honest :) Just thinking of creating estimates in an optimistic mood, all of them getting biased downward ("gonna do that by yesterday boss")... but also someone going on sick leave - many tasks similarly being affected by their absence... indeed, fragile, but this is not meant to be the ultimate bulletproof estimate.

Still, this is a value with uncertainty, that in my hope paints a picture with more, and still useful details - and which you can, by experience, learn to utilize in increasingly effective ways, obtaining a great starting point when trying to gain a reasonably good quantitative understanding of what lies ahead.

If nothing "big and unexpected" (no "shock", no "chain reaction") affects your team, the assumptions should even roughly work. As estimation in software engineering very often fails, I expect this already a big step in the right direction at a low cost.