Problem $3.$Control charts on x and R for samples of size n$-$S are to be maintained on the tensile strength in pounds of a yam. To start the charts, $30$ samples were selected, and the mean and range of each computed. This yields$0=5$A$2$:$0\mathrm{.}577($a$)$ Compute the center line and control limits for the x and R control charts.$($b$)$ Suppose both charts exhibit in$-$control. There is a single lower specification limit of $16$lb$.$ If strength is normally distributed, what fraction of yam would fail to meet specifications?$($e$)$ Is the process capable$($with single LSI$=16$ Ib$)?$ Please discuss what Cp formula is appropriate and analyze process capability $($Cp$)$ for this case.$($d$)$ If the process is out of control, do the process capability analyses in by and e$)$ make sense?