Work out central limit theorem instantly with clear inputs, formula shown and shareable results.
The central limit theorem says the sampling distribution of the mean approaches a normal distribution with the same mean and standard deviation σ/√n, whatever the shape of the population, once n is reasonably large.
Standard error
SE = σ / √n
Standardised sample mean
z = (x̄ − μ) / (σ/√n)
The standard error is 2, so z = 1.5 and the chance of a mean this high or higher is about 6.68%.
Around 30 suffices for mildly skewed populations, but heavily skewed or heavy-tailed data may need hundreds.