Refer to the table Factors for Computing$\_$Control Chart Limits $(3_{?}$ sigma$)$ for this problem.

Your supervisor, Lisa Lehmann, has asked that you report on the output of a machine on the factory floor. This machine is supposed to be producing optical lenses with a mean weight of

$52$ grams and a range of $5$ grams. The following table contains the data for a sample size of $n=6$ taken during the past $3$ hours:

a$)$ What are the $\stackrel{}{x}-$chart control limits when the machine is working properly? Calculate UCL X and LCL X$,$ b$)$ What are the R$-$chart control limits when the machine is working$$ properly? Calculate Upper Range D$4$ and Lower Range D$3$ c$)$ Calculate UCL R and LCL R $($for the R chart$)$ d$)$ Has the process been in control? Yes or no