At a call centre, callers have to wait till an operator is ready to take their call. To monitor this process, $5$ calls were recorded every hour for the $8-$hour working day. The data below shows the waiting time in seconds:

Sample Number

Time $12345$

$9$ a$.$m

$10$

$11$

$12$

$1$ p$.$m

$2$

$3$

$48$

$7$

$11$

$12$

$11$

$7$

$10$

$89$

$10$

$12$

$8$

$10$

$7$

$7$

$1115$

$7$

$10$

$6$

$6$

$10$

$4$

$114$

$6$

$9$

$9$

$14$

$4$

$10$

$1111$

$8$

$10$

$12$

$11$

$11$

$10$

$7$

$($i$)$ Use the data to construct control charts for mean and comments about the process. If process is out of control, then calculate the revised control limits$.$

$($ii$)$ Construct the CUSUM chart when the process is under control and draw the conclusion about the process.

$($iii$)$ If the specification limits as the $8\backslash$pm $2,$ then calculate the process capability index Cpk and impetrate the result.

$($iv$)$ Also find the percentage of calls lie outside the specification limits assuming

that calls follow the normal distribution.