Distribution graph
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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 $$p_2$$.