When defining the properties of normal distribution we saw that they are perfectly defined when we know their average and standard deviation. In particular we know that:

We can go further in order to calculate the percentage of a population outside of tolerance by simply calculating the z number.

The z number represents: the precise standard deviation from the mean value within the sample tolerance.

Once we know the z number we can calculate the off-tolerance percentage by using the Gaussian table.

Let us take the following example:

Let us calculate z_{min} :

We deduct the percentage of parts outside of tolerance min in the Gaussian table:
Let us calculate z_{max} :
We deduct the percentage of parts outside of tolerance min in the Gaussian table:

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