# Math Help - 95% confidence intervals

1. ## 95% confidence intervals

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.

2. ## Re: 95% confidence intervals

The central limit theorem states that when taking samples from a distribution with mean $\mu$ and variance $\sigma^2$ the distribution of the sample tends toward a normal distribution with mean $\mu$ and variance $\frac{\sigma^2}{n}$ as sample size n increases. In the limit as n tends to infinity the sample mean is exactly normally distributed. For large sample sizes (n>30 or n>50) we often assume that the distribution is normal.
Central limit theorem - Wikipedia, the free encyclopedia