$6.7 . Auto pistons at Yongpin Zhou's plant in Shanghai are pro- duced 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 Mean (mm) Range (mm) 156.9 1.2 153.2 4.6 153.6 4.1 155.5 5.0 U A 156.6 4.5 a. What is the value of X ? b. What is the value of R? c. What are the UCL, and LCL, using 30?d. What are the UCLR and LCLR using 30? 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