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. 

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Normal distribution calculator

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.


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.


Step 1: Extract the data.

Raw score = x = 253

Mean = μ = 251

Standard deviation = σ = 5


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


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