[rdlecler1]

Central Limit Theorum tells us that luck will be normally distributed even if you’re sampling from people who work hard. Sure hard work may shift the mean to the right compared to a random sample of the general population, but you still get a normal distribution. Now if being lucky is being in the top 2% from a random population, how much does hard work shift you to the right? You need to shift this distribution pretty far to make the case that work alone can overcome luck.

[alexpetralia]

The sampling distribution of the _sample means_ (averages) will be a normal distribution.

The population distribution need not be normal.