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