Online Normal Distribution Calculator

This calculator for Normal distribution asks to enter three parameters: the known mean of your distribution, its standard deviation and the value you want to explore. In return, the outputs will be the frequency and the probability of the value under study.

Normal Distribution

The shaded area represents the probability of "x’" and its frequency is "y".
The normal probability is approximated using the following formula:

probability = 1 – r(a₁t + a₂t² + a₃t³) + eps

where:
                             a₁ = 0.4361836
                             a₂ = -0.1201676
                             a₃ = 0.9372980
                              auxiliary formula for Normal Distribution code
                             t = 1/(1 + 0.33267x)
                             eps < 10^-5

Example:

The average frequency of a certain type of computers in manufacturing is 2 GHz. The known standard deviation is 0.02 GHz. If the frequency of those computers is normally distributed, what is the probability that a computer runs between 2 GHz and 2.01 GHz?

Run the calculator on the spreadsheet below and enter...

Enter mean: 2
Enter std. deviation: 0.02
Enter variable: 2.01

The output is

Frequency = 0.35207
Probability = 0.69145

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