×

# Normal distribution calculator

## How to use the normal distribution calculator?

Follow the below steps to calculate the continuous probability of a raw score or a data set.
• Select the input type “raw score” or “data set”
• In the case of Raw score:
a)    Enter the Raw score
b)    Enter the Population Mean
c)    Enter the Standard deviation
• In the case of the Data set:
a)    Enter the Data set X
• Click on the “calculate” button to calculate the result
• To erase all inputs, simply hit the “Reset” button.
• You can Load default examples by clicking on the “Sample example” button.

## Normal distribution calculator:

The normal distribution calculator calculates the probability density function (f), if you enter a data set, the normal distribution calculator first calculates the mean, raw score, and standard deviation of the data set after that it will calculate the probability density function.

## What is Normal distribution in statistics?

The normal distribution AKA Gaussian distribution is a continuous probability distribution, it describes the probability of a variable, it is a bell-shaped distribution.

## Formula of Normal distribution:

• “f(x)” is the probability density function.
• “σ” is the standard deviation
• “μ” is the population mean
• “e” is the Euler’s constant.

## Examples:

In this section, we’ll cover the method of calculating the probability density function using the normal distribution.

Example 1:

Calculate the probability density function if Raw score = 253, Mean = 251, and Standard deviation = 5.

Solution:

Step 1: Extract the data.

Raw score = x = 253

Mean = μ = 251

Standard deviation = σ = 5

Formula:

F(x) = {1 / σ*2√π} e -(x - μ)2 / 2σ2

Step 2: Enter the values in the above formula.

F (253) = {1 / 5 √2(3.14159)​}​ * 2.718 −(253−251)2​ / 2(5)2

F (253) = {1 / 5 √6.283​1)​}​​ * 2.718−(2)2​ / 2(25)

F (253) = {1​ / 5(2.507)} * 2.718-4​/50

F (253) = 12.5331​ * 2.718-0.08

F (253) = 0.0798 * 0.9231

F (253) = 0.0737