e-Statistics

Critical Value

Suppose that a random variable $ X$ has the normal distribution with mean $ \mu =$ and standard deviation $ \sigma =$ . Then we can calculate the critical value
$ z_\alpha =$ with level $ \alpha =$
The value $ z_\alpha$ determines the tail probability $ P(X > z_\alpha) = \alpha$. In other words the critical value $ z_\alpha$ represents the $ (1-\alpha)$-th percentile.