Refer to Table S6.1 - Factors for Computing Control Chart Limits (3 sigma) for this problem. Auto pistons at Wemming Chung's plant in Shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. From sample sizes of 10 pistons produced each day, the mean and the range of this diamete have been as follows: Day Range R (mm) 4.2 Mean x (mm) 156.9 153.2 153.6 155.5 156.6 4.6 4.1 or A WN 5.0 4.5 a) What is the value of ? x= mm (round your response to two decimal places). b) What is the value of R? R= mm (round your response to two decimal places). c) What are the UCL; and LCL; using 3-sigma? Upper Control Limit (UCL-) = mm (round your response to two decimal places). Lower Control Limit (LCL-) = mm (round your response to two decimal places). d) What are the UCLR and LCLR using 3-sigma? e) If the true diameter mean should be 155 mm and you want this as your center (nominal) line, what are the new UCL; and LCL:? Upper Control Limit (UCL-) = mm (round your response to two decimal places). Lower Control Limit (LCL;) = mm (round your response to two decimal places)