There are two machines for sale that you are considering purchasing for your sawmill to produce hardwood flooring. You want to find the one that has a higher process capability index, or Cpk. The goal is to produce flooring that is between 46 and 50 millimeters thick. The first machine is more accurate on average, producing to a mean of 48 millimeters...but unfortunately it has more variation with a standard deviation of 7 millimeters. The second machine is not as accurate, with a mean of 47mm, but does deliver a more consistent output, with standard deviation of 3mm. [ Select] What is the Cpk of machine 1?
[Select] What is the Cpk of machine 2?
[ Select] If your goal is to be capable', what would you do?
[ Select] If (somehow) you could combine the best of both machines (the centering or average of machine 1 coupled with the constancy or standard deviation of machine 2, what would the Cpk be?