An automatic lathe machine turns out round hammer handles with a specified shank diameter of 20.00+0.06 mm. The process has been operating in control at an estimated u of 20.00mm and an "Mean R" of 0.03 mm. The sample size is nine. a) Calculate the "Mean X chart" and "R chart"control limits (limits of all six zones). (20 points) b) If the mean of the process shifts to 20.04 mm, compute the Type II error probability that the shift will not be detected on the first sample of 9 items drawn after it occurred. (15 points) c) What proportion of defective products is being produced at this new value of u assuming that the product is normally distributed? (15 points)