This is also very unlike the outcome of donating to a charity, which I can believe is approximately log-normal.
This can’t be right, because log-normal variables are never negative, and charitable interventions do backfire (e.g. Scared Straight, or any health-care program that promotes quackery over real treatment) a non-negligible percentage of the time.
That raises an interesting question: is it possible to base a moral code only on what’s true in all possible worlds that contain me?