a$-1.$ Construct a control chart with three$-$sigma limits for the number of scratches per $6$m $\backslash$times $2$m stainless steel sheet based on the following data. $($Do not leave any empty spaces; input a $0$ wherever it is required. Round the final answers to $2$ decimal places.$)$

Observation

$1234567891011121314$

Number of scratches $23101320213120$

UCLc LCLc

Control Limits

a$-2.$ Is the process in control?

multiple choice $1$

Yes

No

b$.$ If a new sheet has five defects, using the control chart of part a$,$ has the process changed?

multiple choice $2$

Yes

No