Refer to Table 56.1-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 diameter have been as follows: a) What is the value of x? mm (round your response to two decimal places). Mean x Day (mm) Range R (mm) 1 154.9 4.2 2 155.2 4.4 3 151.6 4.1 4 153.5 4.8 5 156.6 4.7 Definition Sample Mean Factor, Upper Range, Size, n A D Lower Range Dy 2 1.880) 3.268 0 3 1.023 2.574 0 4 0.729 2.282 0 5 0.577 2.115 0 6 0.483 2.004 0 7 0.419 1.924 0.076 8 0.373 1.864 0.136 9 0.337 1.816 0.1041 10 0.308 1.777 0.223 12 0.266 1.716 0.284 Print Done X b) What is the value of R? 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 UCL and LCLR using 3-sigma? Upper Control Limit (UCLR) = Lower Control Limit (LCLR) = mm (round your response to two decimal places). mm (round your response to two 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). Lower Control Limit (LCL) = mm (round your response to two decimal places)