Exercise $7\mathrm{.}38$ Algo

Consider a normally distributed population with mean $=95$ and standard deviation $=17.$

a$.$ Calculate the centerline, the upper control limit $($UCL$),$ and the lower control limit $($LCL$)$ for the $\stackrel{}{x}$ chart if samples of size $5$ are used. $($Round the value for the centerline to the nearest whole number and the values for the UCL and LCL to $2$ decimal places.$)$

$\backslash$table$[[,],[$Centerline$,],[$Upper Control Limit,$],[$Lower Control Limit,$]]$

b$.$ Calculate the centerline, the upper control limit $($UCL$),$ and the lower control limit $($LCL$)$ for the $\stackrel{}{x}$ chart if samples of size $10$ are used. $($Round the value for the centerline to the nearest whole number and the values for the UCL and LCL to $2$ decimal places.$)$

$\backslash$table$[[,],[$Centerline$,],[$Upper Control Limit,$],[$Lower Control Limit,$]]$

c$.$ Discuss the effect of the sample size on the control limits$.$