# Hypergeometric Distribution Calculator

The calculator will find the simple and cumulative probabilities, as well as the mean, variance, and standard deviation of the hypergeometric distribution.

## Your Input

**Calculate the various values for the hypergeometric distribution with $$$N = 20$$$, $$$K = 15$$$, $$$n = 12$$$, and $$$k = 8$$$.**

## Answer

**Mean: $$$\mu = n \frac{K}{N} = 12 \frac{15}{20} = 9$$$A.**

**Variance: $$$\sigma^{2} = n \frac{K}{N} \frac{N - K}{N} \frac{N - n}{N - 1} = 12 \frac{15}{20} \frac{20 - 15}{20} \frac{20 - 12}{20 - 1} = \frac{18}{19}\approx 0.947368421052632.$$$A**

**Standard deviation: $$$\sigma = \sqrt{n \frac{K}{N} \frac{N - K}{N} \frac{N - n}{N - 1}} = \sqrt{12 \frac{15}{20} \frac{20 - 15}{20} \frac{20 - 12}{20 - 1}} = \frac{3 \sqrt{38}}{19}\approx 0.973328526784575.$$$A**

**$$$P{\left(X = 8 \right)}\approx 0.255417956656347$$$A**

**$$$P{\left(X \lt 8 \right)}\approx 0.051083591331269$$$A**

**$$$P{\left(X \leq 8 \right)}\approx 0.306501547987616$$$A**

**$$$P{\left(X \gt 8 \right)}\approx 0.693498452012384$$$A**

**$$$P{\left(X \geq 8 \right)}\approx 0.948916408668731$$$A**