QUESTION 1: Process Capability Index (20 points) Steel Factory Inc. has produced steel rods for machinery components. To ensure that the production meets the quality 99.7% of the time, the operation managers take 6 days of diameter measurements, where the result is shown in the below table. Measurement Day in mm 13.029 13.297 13.132 12.674 5 13.177 13.003 1 2 3 4 6 Target value = 13 mm. The factory has set an Upper Tolerance Limit of 14mm and a Lower Tolerance Limit of 12 mm. a. Calculate the mean of the measurements above. (4 points). b. Calculate the standard deviation for the measurement above. You can use a manual calculation or the Excel STDEV.S function (4 points). C. Calculate the Process Capability Index of this process (4 points) d. Can the process meet the quality requirement? Explain your answer (4 points) e. What would the standard deviation have to be to achieve the Six Sigma quality level? (4 points)