The central limit theorem states that the probability distribution of a rescaled sample mean converges, in some conditions, to a normal distribution. The theorem has gone through numerous iterations and variations throughout the history of statistics and probability theory and as such, there exists several different variations.
> [[convergence in distribution|converge in distribution]] to a normal distribution $\mathcal{N}(0,1)$: > $$\frac{\bar{X}_{n}-\mu}{\sigma/\sqrt{ n }}\xrightarrow{d}\mathcal{N}(0,1)