>"In order to estimate what is the true mean of our variants statisticians rely on the Central Limit Theorem (CLT) 6 which states that the sampling distribution of any statistic will be normal or nearly normal, if the sample size is large enough."

Wow, no. This is a very dangerous misconception. First sentence of the wikipedia page gives a much better definition:

"In probability theory, the central limit theorem (CLT) states that, given certain conditions, the arithmetic mean of a sufficiently large number of iterates of independent random variables, each with a well-defined expected value and well-defined variance, will be approximately normally distributed, regardless of the underlying distribution."

https://en.wikipedia.org/wiki/Central_limit_theorem