The operations manager of a large manufacturer received a certain number of complaints during the last two weeks.

a$-1.$ Construct a control chart with three$-$sigma limits for the number of complaints received each day using the following data. $($Round the final answers to $2$ decimal places. Do not leave any empty spaces; input a $0$ wherever it is required.$)$

Day

$1234567891011121314$

Number of complaints $4101489651213764210$

UCLc LCLc

Control Limits

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

multiple choice $1$

Yes

No

b$.$ If $16$ complaints are received today $($day $15),$ using the control chart of part a$,$ is there a change in the average number of complaints per day?

multiple choice $2$

Yes

No