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LSL, USL and CpK

Please help with the following problem.

A data set contains 16 measurements as follows:

1525; 1561; 1541; 1532; 1499; 1551; 1554; 1528; 1514; 1548; 1534; 1505; 1500; 1538; 1529; 1519

the calculated mean = 1530 and the calculated std deviation = 19

The USL and LSL are respectively 1560 and 1510 and I, therefore, derive a CpK = 0.526

I know how to derive the normal distribution curve by plotting the probability and/or z-score for problem.....and I know how to derive the process sigma from the calculated z-score.

But what I do not know, and this is what the problem asks, is to explain the relationship between CpK and process sigma (for instance, why does a CpK of 1.33 equate to process sigma of 4)?

And in my example above, how would I equate my derived CpK to a process sigma value?

Solution Summary

LSL, USL and CpK are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question. Step by step calculations are provided in the solution.