Good evening everyone,
I am currently doing a self-study on CLT and was working on an exercise which asks if the following statement is true or false
CLT guarantees that the population mean is normally distributed whenever sample size is sufficiently large.
I can understand that this statement is False, but I am pretty weak with the concept, thus will like to take this opportunity to validate my thoughts.
CLT does not guarantee that the population mean is normal, instead it allows us to treat a population as normal if a given population size is large enough. Also, the size of the sample will not affect the actual distribution of the population, but rather simply gives us a more accurate approximation.
Appreciate if seniors and exports here can give me some guidance.