Hypergeometric Distribution Calculator

Hypergeometric distribution calculator is a tool that is used to compute the mean, standard deviation, and variance of the entered data rendering the properties of Hypergeometric distribution.

What is hypergeometric distribution?

A hypergeometric distribution, which simulates success rates in a random sample taken from a limited population without replacement, is a probability distribution. It makes the supposition that there are two different kinds of objects in the population: successes and failures.,

The formula of hypergeometric distribution:

We can calculate the hypergeometric distribution by the following formula:

Hypergeometric distribution formula

N stands for Population size
K stands for the number of successful states in population.
(K) Number of success states in the sample.
n stands for sample size.

How to calculate the value of hypergeometric distribution?

Below example will help you to learn how to calculate the value of a hypergeometric distribution.

Example

Compute the value of hypergeometric distribution when N = 44, K = 22, n = 7, and k = 5.

Solution:

First, we find the mean

Step 1:

Mean = µ = n × (K / N)

µ = 7 (22 / 44)
µ = 7 × 0.5

µ = 3.5

Step 2:

Now we compute the variance
σ² = {n × (K / N)} {(N - K) / N} × {(N - n) / (N - 1)}

σ²= 7× (22 / 44) / × (44−22 / 44) × (44−7/ 44 -1)

σ² = 7 × 0.5 × 0.5 × 0.8605

σ² = 1.5058

Step 3:

To Compute the standard deviation, we take the square root of the variance.

√σ² =√ 1.5058

σ = 1.2271

Step 4:

Compute the probability

P (X = k)

P (X = 5) = 0.1587

P (X ≥ k):

P (X ≥ 5) = 0.206

P (X > k):

P (X > 5) = 0.0473

P (X ≤ k):

P (X > 5) = 0.9527

P (X < k):

P (X < 5) = 0.794

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