Question $11$

$10p$

The overall average on a process you are attempting to monitor is $60\mathrm{.}0$ units. The process population standard deviatio is $1\mathrm{.}84.$ Sample size is given to be $16.$

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

Upper Control Limit $($UCLx$)=$ units $($round your response to two decimal places$).$

Lower Control Limit $(LCLx)=$ units $($round your response to two decimal places$).$

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

Upper Control Limit $($UCL $x)=$ units $($round your response to two decimal places$).$

Lower Control Limit $(LCLx)=$ units $($round your response to two decimal places$).$

How do the control limits change?

Choose possible answer $1,2,$ or $3$ below

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

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

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