+1. I wrote myself a script that does this with distributions based on my personal time tracking data for doing certain tasks.

More concretely, I sample with replacement N times from the empirical distributions of each step, then sum the steps to get N “samples” from the total distribution.

This is called bootstrapping: https://en.m.wikipedia.org/wiki/Bootstrapping_(statistics)

It isn’t too hard to do, and I can confirm that it works reasonably well.