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To calculate the probability of any data using hypergeometric distribution calculator, follow the below steps:

- Enter the population size (N)
- Enter the number of success states in population (K)
- Enter the sample size (n)
- Enter the number of success states in sample (k)

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The Hypergeometric distribution calculator is used to calculate the probability of a raw data, it also calculates mean, standard deviation, and variance of the entered data according to the properties of Hypergeometric distribution.

Generally, in statistics and probability theory, the hypergeometric distribution refers to a discrete probability distribution of success.

To calculate the probability of success using Hypergeometric distribution, we use the following formula:

- N is the population size
- K is the number of successes
- n is the number of occurrences
- k is the number of observed successes

There are three properties of the hypergeometric distribution

The mean of the hypergeometric distribution can be calculated by using the following formula:

- n is the number of occurrences
- K is the number of successes
- N is the population size

Standard deviation is a property of the hypergeometric distribution, it can be calculated as:

The variance of hypergeometric distribution can be calculated by using the following formula:

In this section, we’ll cover the step-by-step calculations of probability using the hypergeometric distribution.

**Example 1: **

Calculate the values of hypergeometric distribution if N = 54, K = 22, n = 17, and k = 7.

**Solution: **

**Step 1:** Calculate mean

μ = n * (K / N)

μ = 17 * 22 / 54

μ = 187/27

μ = 6.926

**Step 2:** Calculate variance:

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

σ^{2}_{ }= {17 * (22 / 54)} * {(54 - 22) / 54} * {(54 - 17) / (54 - 1)}

σ^{2}_{ }= 110704 / 38637

σ^{2}_{ }= 2.8652

**Step 3:** Calculate the probability:

P (X = 7) ≈ 0.233327502982322

P (X < 7) ≈ 0.402610817520716

P (X <= 7) ≈ 0.635938320503037

P (X > 7) ≈ 0.364061679496963

P (X >= 7) ≈ 0.597389182479284

*Hypergeometric Distribution: Uses & Formula* | Statistics by Jim.

*Hypergeometric distribution*| WallStreetMojo.