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 $50$ grams and a range of $3\mathrm{.}5$ grams. The following table contains the data for a sample size of n$=6$ taken during the past $3$ hours: Set the control limits for this process for the x$-$chart when the machine is working properly.

$[$ UCL$\_$x$^-=51\mathrm{.}69$ grams $($round your response to two decimal places$).$; LCL$\_$x$^-=48\mathrm{.}30$ grams $($round your response to two decimal places$).]$