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 $12345678910$

IRREGULARITIES $3262656446$

a$.$ Determine the c$,$ Sp$,$ UCL and LCL for a c $-$chart with z $=2.($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, five, five, and five irregularities. Is the supplier process under control?

yes

no