Show all steps in your detailed step$-$by$-$step calculations and the right units of measures in your calculations and all answers. Draw both charts $($using Word or Excel$)$ and indicate the target $($mean$),$ the lower control limit $($LCL$)$ and Upper control limit $($UCL$)$ and mark the out of control points. Be sure your ALL your work is typed and submitted in a regular software such as Word, Excel, PPT$,$ PDF$,$ etc. $($not handwritten or scribbled$)$ and presented in an organized and easy to read format Problem $3\mathrm{.}1$ : The Great Lakes Company, a grocery store chain,

purchases apples from a produce distributor in Ontario. The grocery

company has an agreement with the distributor that shipments

of $10,000$ apples will have no more than $2\%$ defectives $($i$.$e$.,$ severely

blemished apples$),$ although it will accept shipments with up to a

maximum of $8\%$ defective. The probability of rejecting a good lot is

set at $0\mathrm{.}05,$ whereas the probability of accepting a bad$-$quality lot is

$0\mathrm{.}10.$ Determine a sampling plan that will approximately achieve these

quality$-$performance criteria, and the operating characteristic curve