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Problem $13-8($Algo$)$

A shirt manufacturer buys cloth by the $100-$yard roll from a supplier. For setting up a control chart to manage the irregularities $($e$.$g$.,$ loose threads and tears$),$ the following data were collected from a sample provided by the supplier.

$\backslash$table$[[$SAMPLE$,1,2,3,4,5,6,7,8,9,10],[$IRREGULARITIES$,5,5,5,5,1,6,7,3,5,5]]$

a$.$ Determine the $\frac{?}{\text{b}\text{a}\text{r}}(c),S_p,CL$ and LCL for a $c-$chart with $z=2.($Leave no cells blank. Round up any negative LCL value to $"$O$".$ Round your answers to $2$ decimal places.$)$

Answer is complete but not entirely correct.

$\backslash$table$[[],[c,4\mathrm{.}30$