for $15$ samples.

$\backslash$table$[[$Sample$,\backslash$table$[[$Number of$],[$Defects$]],$Sample,$\backslash$table$[[$Number of$],[$Defects$]],$Sample,$\backslash$table$[[$Number of$],[$Defects$]]],[1,8,6,5,11,4],[2,7,7,6,12,8],[3,4,8,8,13,5],[4,7,9,7,14,5],[5,3,10,6,15,2]]$

a$.$ Assuming Janice Sanders is willing to use three$-$sigma control limits$,$ construct the upper and lower control limits$.$

The $UC{L}_p$ equals $$ and the $LC{L}_p$ equals $($Enter your responses rounded to four decimal places. If your answer for $LC{L}_p$ is negative, enter this value as $0..)$

b$.$ Based on your control limits and the data in the table, what can you conclude about the waiting time of the patients?

A$.$ All of the sample proportions are within the control limits and there are no unusual patterns, so the process is in control.

B$.$ At least one of the sample proportions is below the lower control limit$,$ so the process is not in control.

C$.$ The p$-$chart shows a significant upward trend, so the process is not in control.

D$.$ The p$-$chart shows a significant change in the wait times, so the process is not in control.

E$.$ At least one of the sample proportions is above the upper control limit$,$ so the process is not in control.