# Normal Distribution Calculator

 Enter mean μ = Enter standard deviation σ =

## Probability Density Function

 p(x) = $$\frac{1}{\sqrt{2\pi\sigma^2}}e^\frac{-(x-\mu)^2}{2\sigma^2}$$ p()

## Cumulative Distribution Function

 F(a) = $$P(x\leq a)$$ = $$\int_{-\infty}^{a}p(x)\;dx$$ F() 1 - F(a) = $$P(x > a)$$ = $$\int_{a}^{\infty}p(x)\;dx$$ 1 - F() F(b) - F(a) = $$P(a \leq x \leq b)$$ = $$\int_{a}^{b}p(x)\;dx$$ F() - F()

This calculator gives the probability that a random variable with normal distribution and given mean and standard deviation produces a given value, or value within the specified range.