Please show specific hand calculations.

1.) REQUIRED PROBLEM S6.7 on page_268 [20 points) (NOTE: This is similar to Problem S6.6 X-Bar & R-Bar Charts done in lecture.) (a.) Do Problem 56.7 on page 268 of Heizer and Render BY HAND. Evaluate all components of equations for X-Bar Charts on page 249 of (S6-3) & (S6-4), and all components of equations for Range Charts on page 250 of (S6-5) & (S6-6). Evaluate part (e) BY HAND using same equations on page 249 for X-Bar Charts of (S6-3) & (S6-4). (b.) Do Problem S6.7 on page 268 using POM software and check your answers found in parts (a.). (b.), (c.), (d.) & (e.) above by hand. Provide printouts of both numerical and graphical output of using POM software with YOUR NAME & Problem S6.7 in Title Bar. S6.7 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 MEAN (MM) 156.9 RANGE (MM) 1 4.2 2 46 1532 153.6 3 4.1 4 155.5 50 5 156.6 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? Plot the data. d) What are the UCLR and LCL R, using 30? Plot the data. c) 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 ? PX