Management at ASADO restaurant near VCU is in process of establishing a quality control system for the time it takes to initially make contact with a table of patrons. Three sample times were taken on five successive days following the same sampling plan with the following data table being the result. The activity times of each encounter is noted in the table below $($all times listed are in seconds$)$:

Service Encounter Time $1$ Time $2$ Time $3$

Day $1200150175$

Day $212085105$

Day $38393130$

Day $468150145$

Day $51109075$

In the above case, assume you calculated your average process range is $40\mathrm{.}0$ and the overall process average processing time is $100.$ What is the upper and lower control limits for the x$-$bar chart?

UCL $=$ X$-$bar $+$ A$2$ x R$-$bar

LCL $=$ X$-$bar $-$ A$2$ x R$-$bar