Description
For the normal distribution, this calculator gives the areas of the distribution function for each of the 3 complementary intervals partitioned by the 2 user-provided values of \(x_1 \le x_2\). Thus, the values (derived from the quantile function \(x = F^{-1}(p)\)) corresponding to the left (\(x_1 = F^{-1}(p_1)\)), between (\(F^{-1}(p_2)-F^{-1}(p_1)\)) and right (\(1-F^{-1}(p_2)\)) regions are obtained for each given pair of critical values (\(x_1 \le x_2\)) or probability values (\(p_1 \le p_2\)). Note that the user can specify either the critical or the probability values and the webapp computes the other (\(p_3 = 1-p_2\)). The mean \(\mu\) and standard deviation \(\sigma\) of the distribution can be varied with the input controls, as can the variables \(x_1\), \(x_2\), \(p_1\), and \(p_2\).