The overall average on a process you are attempting to monitor is $50\mathrm{.}0$ units. The process population standard deviation is $1\mathrm{.}84.$ Sample size is given to be $16.$

a$)$ Determine the $3-$sigma $\stackrel{}{x}-$chart control limits$.$

Upper Control Limit $(($:$UC{L}_{\stackrel{}{x}}\}$ units $($round your response to two decimal places$).$

Lower Control Limit $(LC{L}_{\frac{?}{\text{b}\text{a}\text{r}}()})=,$ units $($round your response to two decimal places$).$

b$)$ Now determine the $2-$sigma $\stackrel{}{x}-$chart control limits$.$

Upper Control Limit $(($:$UC{L}_{-}^{-}\}$ units $($round your response to two decimal places$).$