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


$$$P\left(-0.975 \leq X \leq 0.975\right)=0.95$$$