Re: 95% confidence intervals

The central limit theorem states that when taking samples from a distribution with mean $\displaystyle \mu$ and variance $\displaystyle \sigma^2$ the distribution of the sample tends toward a normal distribution with mean $\displaystyle \mu$ and variance $\displaystyle \frac{\sigma^2}{n}$ 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