A machine is working to a specification of $12\mathrm{.}58\backslash$pm $0\mathrm{.}05.$ A study of $50$ consecutive piecesshows the following measurement put in $10$ groups of $5$ each.$($a$)$ Determine the control limits for average and range charts. $($b$)$ Plot the data and interpret the results. $($c$)$ Determine the process capability. $($d$)$ Does it appear that machine is capable of meeting the specifications requirements. Ifnot determine the percentage of rejection.