The data population shown below has the specification limit range of 50.4 to 51.6. The data sample is as follows: 50.6, 50.7, 50.8, 50.8, 50.6, 50.6, 50.4, 50.5, 51.2, 51.6, 51.3, 51.2 [Note: In answering the following questions, you may use the statistics functions available on your scientific calculator. However, if you do so, you must still give a brief explanation of the steps/work. Write formulas wherever applicable.]

a. Calculate the mean for the data sample.

b. Calculate the variance of the sample

c. Calculate the standard deviation for the data sample.

d. Find Cp for this data.

e. Find Cpk for this data.

f. Draw a graph of the process showing mean, USL, LSL, and the sigma values at which failure starts happening.