# Normal Probability Calculator

\[ P( x_0 \lt X \lt x_1 ) = \displaystyle \int_{x_0}^{x_1} \dfrac{1}{\sigma \sqrt{2 \pi}} e^{ - \dfrac{(x-\mu^2)}{2 \sigma^2}} dx \]

\[ P( X \lt x_0 ) = \displaystyle \int_{-\infty}^{x_0} \dfrac{1}{\sigma \sqrt{2 \pi}} e^{ - \dfrac{(x-\mu^2)}{2 \sigma^2}} dx \]

\[ P( X \gt x_0 ) = \displaystyle \int_{x_0}^{\infty} \dfrac{1}{\sigma \sqrt{2 \pi}} e^{ - \dfrac{(x-\mu^2)}{2 \sigma^2}} dx \]

There are no closed form solutions to the above integrals and they are therefore computed numerically.

We present three calculators that compute the three probabilities given above.

Enter the mean and standard deviation as real numbers; the standard deviation must be positive.

Mean , Standard Deviation =

Decimal Places =P ( \( \lt X \lt \) ) ,

P ( \( X \lt \) ) ,

P ( \( X \gt \) ) ,