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:

**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

σ^{2} = {n × (K / N)} {(N - K) / N} × {(N - n) / (N - 1)}

σ^{2 }= 7× (22 / 44) / × (44−22 / 44) × (44−7/ 44 -1)

σ^{2} = 7 × 0.5 × 0.5 × 0.8605

**σ**^{2} = 1.5058

**Step 3:**

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

√σ^{2} =√ 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