5.2. Find the percentage below the lower specification
The Z value for the lower specification is found by subtracting the lower specification from the overall average, and then dividing by the estimated standard deviation. The Z value for the lower specification is denoted as Zlower. The lower specification for the example is 0, the overall average is 10.00, and the estimated standard deviation is 2.00. Thus, the value for Zlower for the example is:
This means that the lower specification is located 5.00 estimated standard deviations away from the overall average. Look up the Z value in the standard normal distribution table as previously described. Since the table shows Z values up to only 4, the proportion and percentage outside of the specification is taken as 0. If any of the data is outside the specification, add the percentage to the diagram.
The above article is an excerpt from the "Operational definition" chapter of Practical Tools for Continuous Improvement Volume 2 Statistical Tools.