The overall average on a process you are attempting to monitor is $55\mathrm{.}0$ units. The process population standard deviation is $1\mathrm{.}84.$ Sample size is given to be $4.$

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

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

Lower Control Limit $(LC{L}_{\stackrel{}{x}})=$ units $($round your response to two decimal places$).$

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

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

Lower Control Limit $(LC{L}_{\stackrel{}{x}})=$ units $($round your response to two decimal places$).$

How do the control limits change?

A$.$ The control limits are tighter for the $2-$sigma $\stackrel{}{x}-$chart than for the $3-$sigma $\stackrel{}{x}-$chart.

B$.$ The control limits are tighter for the $3-$sigma $\stackrel{}{x}-$chart than for the $2-$sigma $\stackrel{}{x}-$chart.

C$.$ The control limits for the $2-$sigma $\stackrel{}{x}-$chart and for the $3-$sigma $\stackrel{}{x}-$chart are the same.