Normal Distribution Calculator

Calculate probabilities using the normal distribution with customizable mean and standard deviation.

Distribution Parameters

Mean (μ)*

The center of the distribution

Standard Deviation (σ)*

A measure of how spread out the data is from the mean

Select Probability Type

Value (a)*

The probability density function of the normal distribution is:

f(x) = \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2}

Where:

For probability calculations, we use the cumulative distribution function (CDF):

\Phi(x) = P(X \leq x) = \int_{-\infty}^{x} f(t) \, dt

Calculate binomial probabilities.

Work with the Poisson probability distribution.

Calculate hypergeometric probabilities.