In probability theory, the central limit theorem (CLT) establishes that, in many situations, for identically distributed independent samples, the standardized sample mean tends towards the standard normal distribution even if the original variables themselves are not normally distributed.
sampling distribution of the mean
given a population with mean $\mu$ and standard deviation $\sigma$, the sampling distribution of the mean approaches: $$\mathcal{N}(\mu, \frac{\sigma}{\sqrt{n}}) $$ as n, the sample size, increases.
References
- Sampling Distribution https://onlinestatbook.com/2/sampling_distributions/sampling_distributions.html