Normal Distribution Formula

In probability and statistics, the normal distribution or Gaussian distribution or bell curve is one of the most important continuous probability distributions. The normal distribution is defined as the probability density function f(x) for the continuous random variable, say x, in the system. A normal distribution is a very important statistical data distribution pattern occurring in many natural phenomena, such as height, blood pressure, lengths of objects produced by machines, etc. Here, we are going to discuss the normal distribution formula and examples in detail.

Normal Distribution Formula

For a random variable x, with mean “μ” and standard deviation “σ”, the probability density function for the normal distribution is given by:

Normal Distribution Formula:

Where 

μ = Mean

σ = Standard deviation

x = Normal random variable

Solved Example on Normal Distribution Formula

Example: 

Find the probability density function for the normal distribution where mean = 4 and standard deviation = 2 and x = 3.

Solution:

Given:

Mean,μ = 4

Standard deviation, σ = 2

Random variable, x = 3.

We know that the normal distribution formula is:

Now, substitute the values in the formula, we get

Therefore, the probability density function for the normal distribution is 0.17603.

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