An automatic lathe (a machine in which work is rotated about a horizontal axis and shaped by a fixed tool) produces rollers for roller bearings, and statistical process control charts are used to monitor the process. The central line of the chart for the sample means it is set at 8.50 and for the range at 0.31 mm. The process is in control, as established by samples of size 5. The upper and lower specifications for the diameter of the rollers are (8.50 + 0.25) and (8.50 - 0.25) mm, respectively. Your client would like to reduce the tolerance, but according to the contract agreement, they would pay for the tooling which they are reluctant to do at this stage, and would rather accept a few nonconforming parts, provided the level is under 5%. a) Calculate the control limits for the mean and range charts