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 $Z$.
