Please answer Parts C, D, and E.

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: Day 1 2 3 Mean x (mm) 158.9 155.2 155.6 157.5 158.6 Range R (mm) 4.2 4.8 3.9 4.8 4.3 4 5 a) What is the value of X? = x= 157.16 mm (round your response to two decimal places). b) What is the value of R? R= = 4.40 mm (round your response to two decimal places). c) What are the UCL; and LCL; using 3-sigma? Upper Control Limit (UCLX) = mm (round your response to two decimal places). 1 Definition x Sample Size, n Lower Range, D3 0 2 0 0 0 Mean Factor, A2 1.880 1.023 0.729 0.577 0.483 0.419 0.373 0.337 0.308 0.266 Upper Range, D4 3.268 2.574 2.282 2.115 2.004 1.924 1.864 1.816 1.777 1.716 8 9 10 12 0 0.076 0.136 0.184 0.223 0.284 d) What are the UCL Subscript Upper RUCLR and LCL Subscript Upper RLCLR using 3-sigma? Upper Control Limit (UCL Subscript Upper RUCLR) = nothing mm (round your response to two decimal places). Lower Control Limit (LCL Subscript Upper RLCLR) = nothing 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 Subscript x overbarUCLX and LCL Subscript x overbarLCLx? Upper Control Limit (UCL Subscript x overbarUCLx) nothing mm (round your response to two decimal places). Lower Control Limit (LCL Subscript x overbarLCLX) nothing mm (round your response to two decimal places)