Normal Distribution Calculator

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 $$$\sigma=1$$$


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