Hypergeometric Distribution Calculator

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

Population size $$$N$$$:

Number of successes in the population $$$K$$$:

Sample size $$$n$$$:

Number of successes in the sample $$$k$$$:

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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

$$$P{\left(X < 8 \right)}\approx 0.0510835913312693$$$A

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

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

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