Normal Distribution Calculator

Calculate probabilities of the normal distribution step by step

For the given mean and standard deviation, the calculator will find various probabilities for the random variable, and vice versa: for the specified probability, it will find the values of the random variable.

If $$$X$$$ is a normally distributed variable with the mean $$$\mu=$$$ and the standard deviation $$$\sigma=$$$, then
$$$P(X \leq$$$ $$$)=?$$$
$$$P(X \geq$$$ $$$)=?$$$
$$$P($$$ $$$\leq X \leq$$$ $$$)=?$$$
$$$P\left ( X \leq ? \right) =$$$
$$$P\left ( X \geq ? \right) =$$$
$$$P \left( -? \leq X \leq ? \right) =$$$
Skip input, if you don't need it.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

Your input: calculate $$$P\left( -? \leq X \leq ? \right)=0.95$$$ with $$$\mu=0$$$ and $$$\sigma=1$$$


$$$P\left(-1.95996398454005 \leq X \leq 1.95996398454005\right)=0.95$$$