Refer to Table S6.1 - Factors for Computing Control Chart Limits (3 sigma) for this problem. Auto pistons at Wenming 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 diameter have been as follows: 5. Mean x Range R Day (mm) (mm) 1 154.9 4.2 2 151.2 48 3 153.6 3.9 4 155.5 5.2 5 156.6 4.3 a) What is the value of x? X= 154.36 mm (round your response to two decimal places). b) What is the value of R? R= 4.48 mm (round your response to two decimal places). c) What are the UCL; and LCL; using 3-sigma? Upper Control Limit (UCL;) = 155.74 mm (round your response to two decimal places). Lower Control Limit (LCL;) = 152.98 mm (round your response to two decimal places). d) What are the UCLp and LCLp using 3-sigma? Upper Control Limit (UCLp) = mm (round your response to two decimal places). decimal places). 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)