# Standard Normal Variable Z ... I do not understand

#### thedealer

##### New Member

Hi,

This is not a homework question as I have the answer, just trying to figure out the method;

I have a "Normal Distribution Table" infront of me.

Sample mean = 76.8
Standard Deviation = 12.43
n = 40, m = 8 intervals

And below are the defined intervals of the standard normal variable (z).
What I do not understand is how the values 1.15, 0.675, 0.32, 0.00 have been produced. Could someone kindly inform me / show me,

Prob (z < -1.15) = 0.125
Prob (-1.15 < -0.675) = 0.125
Prob (-0.675 < -0.32) = 0.125
Prob (-0.32 < -0.00) = 0.125
Prob ( 0.00 < +0.32) = 0.125
Prob ( 0.32 < +0.675) = 0.125
Prob ( 0.675 < +1.15) = 0.125
Prob ( z > +1.15) = 0.125

Thanks

#### JohnM

##### TS Contributor
z represents the number of standard deviations away from the mean a particular value is:

z = (x - mu)/s

Your table is a smaller version of a normal table that shows the proportion (roughly) of z scores that should fall within particular ranges if the variable follows a normal distribution.

#### thedealer

##### New Member
Thank you for such a quick response.

z = (x - mu)/s

I googled those terms, but still can't seem to fathem it.

would X be 76.8, and S = 12.43.

How would I get the value mu.

Could you run through the first line or two, I would be extremly grateful (i.e. obtaining value -1.15 and -0.675).