$$

The overall average on a process you are attempting to monitor is $55\mathrm{.}0$ units. The process population standard deviation is $1\mathrm{.}72.$ Sample size is given to be $4.$

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$).$

B$)$ determine the $2-$sigma x $-$ chart control limits $-$ upper$\_\_\_\_\_\_$

lower $\_\_\_\_\_$

C$)$ how do the control limits change?