Central Limit Theorem Calculator

Calculate the sampling distribution of the mean using the Central Limit Theorem

Population Mean (μ):

Population Standard Deviation (σ):

Sample Size (n):

Sample Mean (x̄) - Optional:

About the Central Limit Theorem

The Central Limit Theorem states that the sampling distribution of the sample mean approaches a normal distribution as sample size increases, regardless of the population distribution.

Key Formulas:

Standard Error: SE = σ / √n
Z-Score: z = (x̄ - μ) / SE
Rule of thumb: n ≥ 30 for CLT to apply