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.

a$.$ Determine the $\frac{?}{\text{b}\text{a}\text{r}}(c),S_p,$ UCL 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.$)$

b$.$ Suppose the next five rolls from the supplier had three, two, five, five, and five irregularities. Is the supplier process under control?

Yes

No