So don’t forget, the normal distribution is in general determined by its mean and standard deviation. The cases of a regular normal distribution or of a standard normal distribution can all be handled with the above probability calculator. One very important special case consists of the case of the standard normal distribution, which corresponds to the case of a normal distribution with mean equal to \(\mu = 0\), and standard deviation equal to \(\sigma = 1\). If you need to compute \(\Pr(3 \le X \le 4)\), you will type “3” and “4” in the corresponding boxes of the script. Change the parameters for a and b to graph normal distribution based on your calculation needs. This not exactly a normal probability density calculator, but it is a normal distribution (cumulative) calculator. Using the above normal distribution curve calculator, we are able to compute probabilities of the form \(\Pr(a \le X \le b)\), along with its respective normal distribution graphs.