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 $4.$

$$a$)$ Determine the $3-$sigma x$-$chart control limits$.$

Upper Control Limit $($UCLx$)=52\mathrm{.}7652\mathrm{.}76$ units $($round your response to two decimal$$ places$).$

Lower Control Limit $($LCLx$)=47\mathrm{.}2447\mathrm{.}24$ units $($round your response to two decimal$$ places$).$

$$b$)$ Now determine the $2-$sigma x$-$chart control limits$.$

Upper Control Limit $($UCLx$)=?$

$($round your response to two decimal$$ places$).$