The timer has a theoretical precision of 1ms. If I time 1000 repetitions of load_size of 1000, I get the following graph. It shows the precision is indeed 1ms and the distribution has a notable right skew.

I'm thinking of the much simpler case, same input, same system. What I observe is pretty far from Gaussian.
(Run the code for yourself: hastebin.skyra.pw/tizivijire.css )

I've been using log-normal because it only has positive support, is right skewed, and has an easily computible ratio distribution (not true of normal!). Often I'm comparing performance of program X in condition Y vs Z, where we don't care about the absolute difference in runtime, only the ratio.