An automatic lathe machine turns out round hammer handles with a specified shank diameter of 2000006 mm The process has been operating in control at an estimated 2000mm and a Mean R of 003 mm The sample size is nine 

a) Calculate the Mean X chart and R chart control limits (limits of all six zones)

b) If the mean of the process shifts to 2004 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 

c) What proportion of defective products is being produced at this new value of assuming that the product is normally distributed