$\backslash$table$[[\frac{\text{d}\text{a}\text{t}\text{e}}{1},$Yield,,date,Yield,marev il werts,$\backslash$table$[[$le quantht$],[$date$]],\backslash$table$[[$ined for revoo$],[$Yialiq$]],],[\frac{1}{2},230,3,8,170,4,15,260,20],[\sqrt[\phantom{2}]{3},\frac{180}{220},12,9,240,16,16,250,24],[4,\frac{220}{190},20,10,130,5,17,250,16],[5,\frac{190}{280},$II$,11,300,20,78,240,12],[6,\frac{280}{160},16,12,150,5,19,280,16],[7,210,\frac{12}{14},13,260,13,201,230,8],[,,14,14,160,6,,,]]$

$($A$)$ Based on the output of these $20$ days, please establish the trial control limits $($Centerline$,$ UCL and $LCL)$ of the $p$ control chart for date $3,$ date $8$ and date $16.$

$($B$)$ Please use the standardized $($Z$)$ control chart to calculate the $Z$ values $(Z^{\text{'}\text{'}},28,216)$ of date $3,$ date $8,$ and date $16$ respectively? $($:$-10\%\}.$ The