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Hypergeometric Distribution Calculator

A 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.

How to use the hypergeometric distribution calculator?

Follow the steps below to utilize the hypergeometric distribution calculator:

Select the compute type.
Put the population size (N).
Put the number of success states in the population (K).
Put the sample size (n).
Put the number of success states in the sample (k).
Hit the "Calculate" button to compute the input
To enter new values click on the "Reset" button

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.

Applications of hypergeometric distribution:

The Hypergeometric distribution has many applications here we discuss some important applications.

In genetics, the likelihood of finding a specified number of people with a certain genotype in a population is modeled using the hypergeometric distribution.
It is possible to examine the distribution of species in a certain habitat using the hypergeometric distribution.
The hypergeometric distribution may be used to simulate the spread of a disease within a population.
The likelihood that a specific number of deals out of a given number of trades will be successful may be modeled using the hypergeometric distribution in finance.
In sports, the chance of winning a specific number of games can be determined using the hypergeometric distribution.

Example section:

In this section, we will solve the step-by-step example of a hypergeometric distribution.

Example 1:

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