# Hypergeometric Distribution Calculator

## Calculate probabilities of the hypergeometric distribution step by step

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**