(a) Plot of the cdf for the standard normal, $\mathcal{N}(0,1)$. Generated by gauss_plot.ipynb . (b) Corresponding pdf. The shaded regions each contain $\alpha /2$ of the probability mass. Therefore the nonshaded region contains $1-\alpha$ of the probability mass. The leftmost cutoff point is $\Phi ^{-1}(\alpha /2)$, where $\Phi$ is the cdf of the Gaussian. By symmetry, the rightmost cutoff point is $\Phi ^{-1}(1-\alpha /2)=-\Phi ^{-1}(\alpha /2)$. Generated by quantile_plot.ipynb .