The overall average on a process you are attempting to monitor is $50\mathrm{.}0$ units. The process population standard deviation is $1\mathrm{.}72.$ Sample size is given to be $5.$

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

Upper Control Limit $($UCL Subscript x overbar$)=$

$$

enter your response here units $($round your response to two decimal$$ places$).$

Lower Control Limit $($LCL Subscript x overbar$)=$

$$

enter your response here units $($round your response to two decimal$$ places$).$

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

Upper Control Limit $($UCL Subscript x overbar$)=$

$$

enter your response here units $($round your response to two decimal$$ places$).$

Lower Control Limit $($LCL Subscript x overbar$)=$

$$

enter your response here units $($round your response to two decimal$$ places$).$

How do the control limits$$ change?

A$.$

The control limits are tighter for the $3-$sigma x overbar$-$chart than for the $2-$sigma x overbar$-$chart.

B$.$

The control limits for the $2-$sigma x overbar$-$chart and for the $3-$sigma x overbar$-$chart are the same.

C$.$

The control limits are alwasys set at $3-$sigma for an x overbar$-$chart. The idea one might choose a differnt number than $3$ is nonsense.