(Solved): 12. I need EVERY step and each step fully explained with all the correct answers and explanations! ...

The Watson Electric Company produces compact fluorescent light bulbs. The following data on the number of lumens for 40 -watt light bulbs were collected. a) Calculate control limits for an $\stackrel{?}{x}$-chart. b) Calculate control limits for an $R$-chart. c) Is the process in control? d) Since these data were collected, some new employees were hired. A new sample obtained the following readings: $570,603,623$, and 583 . Is the process in control after the new sample data were added to the original table? Note: Use the control limits obtained in parts (a) and (b) above.