**Definition 1**: The **standard normal distribution** is *N*(0, 1)*.*

To convert a random variable *x* with normal distribution *N*(*μ, σ*) to standard normal form you use the following linear transformation:

The resulting random variable is called a z-score. Thus *z* = STANDARDIZE(*x, μ, σ*), as described in Definition 3 and Excel Functions in Expectation.

The z-score provides a standard way to compare statistics based on different normal distributions.

**Property 1**: If *x* is a random variable with normal distribution *N*(*μ, σ*) then the corresponding z-score has normal distribution *N*(0, 1)

Proof: Since is a linear transformation of the form

by Property 1 of Characteristics of Normal Distribution, it follows that *z* has normal distribution of type

**Excel Functions**: Excel provides the following functions for the standard normal distribution:

**NORMSDIST**(*x*) = NORMDIST(*x*, 0, 1, TRUE); the standard normal version of NORMDIST

**NORMSINV**(*p*) = NORMINV(*p*, 0, 1); the inverse of NORMSDIST

Note that NORMSINV(*p*) = the value *x* such that NORMSDIST(*x*, TRUE) = *p*

Excel 2010/2013 provide the following additional functions: **NORM.S.DIST**(*x*, cum), where cum takes the value TRUE or FALSE and **NORM.S.DIST**(*x*, cum) = NORM.DIST(*x*, 0, 1, cum), as well as **NORM.S.INV** which is equivalent to NORMSINV.

Dear Dr. Charles,

Thank you for your helpful website.

Hi Charles!

Your site is very helpful. Thankx for the reply on ANOVA. I have confusion regarding normal distribution of data.

If i collect data from 10 sites (10 replicates each), if i have to check the normal distribution of the data , i check for each site separately or overall data i.e all 10 sites together, or

for an experiment (treatment v control) and with 6 replicates, the normality of the data, is checked for the control and treatment separately, or both together.

Thankx!

Sanitha,

You need to check the normality of each group separately.

Charles

Thankx! Charles.