Control charts for X-bar and R, using a subgroup size of 5, are to be applied to control the critical dimension of a certain manufacturing process. Specifications call for a nominal dimension of 1,250.000 + 0.050 mm. The process is believed to have a of 0.015 mm a) Determine appropriate control limits for the X-bar and R charts. b) After 12 subgroups have been drawn and X-bar and R plotted on the charts, a computation of X- double bar give 1,250.015. What is the probability that a value of X-bar will fall within the limits found in part (a) if this is the true value of the mean setting? What is the probability that all 12 values fall within the control limits?