The central limit theorem states that, for any population with mean μ and standard deviation σ, the distribution of sample means for a sample size of n will have a mean of μ, a standard deviation of σ/√n, and will approach a normal distribution as n increases. This theorem is crucial for inferential statistics because it describes the distribution of sample means regardless of the population's shape, mean, or standard deviation, and it approaches a normal distribution quickly as the sample size increases. Essentially, it helps estimate the distribution of sample means without needing to collect all possible samples.
