Statistics: normal distribution vs standard normal distribution

Tutoring statistics, fundamental ideas about the normal distribution are important. The tutor mentions the difference between normal and standard normal.

I begin about the normal distribution in my post from Nov 17, 2014. That post mentions some familiar concepts about it, such as its symmetry.

To define a normal distribution, one must specify its centre point, aka mean (some people think “average” for “mean”), as well as its standard deviation. The higher the standard deviation, the more spread out the values are.

A normal distribution could have any value for its mean, and any non-negative value for its standard deviation. However, the standard normal distribution has mean=0 with standard deviation=1.

In the old days, when tables were used to look up values pertaining to normal distributions, values from a given normal distribution were standardized to what they would be under the standard normal. Then, only a single table was needed.

Today, calculators and computers typically allow the user to enter their own mean and standard deviation, so standardization is no longer needed in that way.

Source:

Harnett, D.L., Murphy, J.L. (1993). Statistical Analysis for Business and Economics. Addison-Wesley.