$1-$ A machine is working to a specification of $12\mathrm{.}58+-0\mathrm{.}05.$ A study of $50$ consecutive pieces show the

following measurement put in $10$ groups of $5$ each.

$($a$)$ Determine the control limits for $\stackrel{}{x}$ and $R$ charts.

$($b$)$ Plot the data and interpret the results.

$($c$)$ Determine the process capability.

$($d$)$ Does it appear that the machine is capable of meeting the specifications requirements. If not determine

the percentage of rejections.