Every distribution can be standardized.

How we can obtain a standard normal distribution from any normally distributed data set?

• Adding or subtracting values to all data points does not change the standard deviation. We’ve just shifted our graph to the right or left without changing its shape.
• Dividing each and every data point by its standard deviation will change the shape of the graph, but it will still be normally distributed. We get a new set of data with a mean of zero and a standard deviation of one.

Imagine we have a variable X, which follows a Normal Distribution with a mean of 4 and a variance of 9. We want to standardize Z, so what formula do we use for the transformation? Below is the z score.

Every distribution can be standardized. A normal distribution can also be standardized, resulting in a standard normal distribution. Imagine transforming your normal distribution so that the mean is zero and the standard deviation is one.

Get Standard Normal Distribution Example

Next we need to look at the Central Limit Theorem in the next post in the series.