Central Limit Theorem Calculator

Find the sampling distribution of the mean.

Sampling mean 100

Standard error 2.5

Formula: mean stays; SE = σ ÷ √n

Step-by-step with your numbers:

1. Values used:

2. Population mean = 100

3. Population SD = 15

4. Sample size = 36

6. Sampling mean = 100

7. Standard error = 2.5

Did we solve your problem today?

The CLT says sample means become normally distributed as sample size grows.

The math behind it

The sampling distribution of the mean has the same mean and a standard error of σ ÷ √n.

μ 100, σ 15, n 36 → SE = 2.5.

How big must n be?

About 30 is enough for most distributions to look normal.