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 $$P(X \leq$$$ $$)=?$$$$$P(X \geq$$$ $$)=?$$$$$P($$$ $$\leq X \leq$$$$$)=?$$$
$$P\left ( X \leq ? \right) =$$$$$P\left ( X \geq ? \right) =$$$
$$P \left( -? \leq X \leq ? \right) =$$$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 $$\sigma=1$$$

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