# How to Calculate Z Score Values

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#### dbulak

Forgot how to calculate.

I am looking at some information that was given to me.

Exact thickness 125.00
usl+2.00
lsl -2.00

mean 124.99
cpk 1.883
sigma .352

Zusl: 5.721
Zlsl: -5.648
Zmin: 5.648

I haven't been able to come up with where they got th Z vaues from.

I haven't done these calculations for a long time. Can anyone help.

A

#### Atul Khandekar

Z-score tells how many 'sigmas' away a certain value is from the mean in a normal distribution.

For a given value x, zX= (x - Mean)/sigma

zUSL = no of sigmas the USL is away from the mean
= (USL - XBAR) / sigma
= ( 127 - 124.99) / 0.352
= 5.7102

zLSL = no of sigmas the LSL is away from the mean
= (LSL - XBAR) / sigma
= ( 123 - 124.99) / 0.352
= -5.6534
These values are slightly different from the ones you have given. May be bit of rounding-off.

From the Z-table you can calculate the area under the curve and then the Estimated Out-of-spec.

- Atul

Thanks, Atul!

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