$25$

$4$ points

A microbrewery tracks its output in gallons over a five hour period for each of seven days. Their data is in the table below, and they went ahead and calculated the averages and ranges for the individual samples and the overall averages Their data and the factors tables can be found below. Calculate the upper $($LCL$)$ and lower $($UCL$)$ control limits for X bar, and $R$ charts for their process.

$\backslash$table$[[$Dar$,$ ay$,,,,x,],[1,46,49,45,47,48,47\mathrm{.}0],[2,43,52,46,52,44,47\mathrm{.}4],[3,45,55,46,51,43,48\mathrm{.}0]]$