Problem $10-24($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 $\frac{?}{\text{b}\text{a}\text{r}}(c),S_c,$UCL and LCL for a $c-$chart with $z=2.$

Note: Leave no cells blank. Round up any negative LCL value to $"0".$ Round your answers to $2$ decimal places.

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

control?

No

Yes

Please show your work and provide answers!