3. Suppose that we are making an auto part and that the mean length of the part is 5 inches with variance of 0.28 inch squared. We would like to set the upper and lower specification limits so that 99.90% of all sheets of paper fall within the upper and lower specification limits. Moreover, we would like the mean paper width to be centered halfway between the upper and lower specification limits.

a. What should we set the upper and lower specification limits to be? (Assume that the length of the auto part is normally distributed. You may need to use a z-table for this question.)

b. Calculate the Cp and the Cpk of the process