For fun I've done some distribution calculations after a week of ticks (168 ticks of non-fort time with assumed 3.5% probability).

Here are the mentioned probabilities:

SPAWNED 0 => CHANCE 0.25%
SPAWNED 1 => CHANCE 1.53%
SPAWNED 2 => CHANCE 4.64%
SPAWNED 3 => CHANCE 9.32%
SPAWNED 4 => CHANCE 13.93%
SPAWNED 5 => CHANCE 16.58%
SPAWNED 6 => CHANCE 16.34%
SPAWNED 7 => CHANCE 13.71%
SPAWNED 8 => CHANCE 10%
SPAWNED 9 => CHANCE 6.45%
SPAWNED 10 => CHANCE 3.72%
SPAWNED 11 => CHANCE 1.94%
SPAWNED 12 => CHANCE 0.92%
...


Formula used: https://www.youtube.com/watch?v=qIzC1-9PwQo
Sample in Wolfram to play around with yourself: https://www.wolframalpha.com/input/?....035)%5E(168-0) - just replace the "0s" with the number of scientists you want and "168s" with the number of ticks, it will return the chance of having that many successes after that many tries (scientists after ticks).