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.

Sample Irregularities

$13$

$25$

$32$

$46$

$55$

$64$

$76$

$83$

$94$

$105$

Total $43$

a$.$ Using these data, set up a c$-$chart with z $=2.$

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