I have data that is very right skew where I know the sample mean, the sample standard deviation and the sample size. I have calculated a 95% confidence interval for the mean using the following method:

(mean-1.96xESE, mean+1.96xESE) where ESE is estimated standard error.

The question then asks why it doesn't matter whether the distribution of the population is or isn't normal?

Does anyone know the answer? Thanks.