Difference between Normal Distribution and Standard Normal Distrubution

Could anybody help explain the differences between Normal Distributions and Standard Normal Distributions?


Normal distributions can have any mean and any (positive) standard deviation.

The standard normal distribution is the one with mean zero and standard deviation one.

The standard normal distribution is just a normal distribution scaled/standardized by the z-formula.

Entering every xi value of the normal distribution into the z-formula will give you the standard normal distribution which by definition of the z-formula than has a mean of zero and a standard deviation of one. (Basically what you do in standardizing is just shifting the distribution).

Note: The probability of any value xi under the normal distribution and the standard distribution is the same.