CLT for skewed population Use the Sampling Distributions app

CLT for skewed population Use the Sampling Distributions applet by selecting the right skewed population distribution and explain how the variability and shape of the sampling distribution of the sample mean changes as n changes from 2 to 5 to 30. Explain how the central limit theorem describes what you have observed.

Solution

Right skewed population distribution originally.

When n changes from 2 to 5, though right skewed skewness decreases for large sample size.

As n increases to 30 skewness still reduces and we conclude that as n becomes very large this can be assumed as a normal distributon.