## Confidence Interval for Mean

Let `$X_1, X_2, \cdots , X_{n}$`

be a random sample of size $n$ from $N(\mu, \sigma^2)$ with known variance $\sigma^2$.

## Formula

$100(1-\alpha)$% confidence interval for the population mean $\mu$ is

`$\overline{X} - E \leq \mu \leq \overline{X} + E$`

where

`$\overline{X} = \dfrac{1}{n} \sum X_i$`

, is the sample mean,`$E = Z_{\alpha/2} \dfrac{\sigma}{\sqrt{n}}$`

is the margin of error,`$1-\alpha$`

is the confidence coefficient,`$Z_{\alpha/2}$`

is the critical value of $Z$.