$2$The Big Black Bird Company produces fiberglass camper tops. The process for producing the tops must be

controlled so as to keep the number of dimples low. When the process was in control, the defects shown to

the right were found in $10$ randomly selected camper tops over an extended period of time.

a$.$ Assuming $10$ observations are adequate for this purpose, determine the three$-$sigma control limits for dimples per camper top.

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

b$.$ Suppose that the next camper top has $18$ dimples. What can you say about the process now?

A$.$ The number of defects is greater than the upper control limit$,$ so the process is not in control.

B$.$ The number of defects is less than the upper control limit$,$ so it is assumed that the process is in control.

C$.$ The number of defects is less than the upper control limit$,$ so the process is not in control.

D$.$ Since the number of defects is close to the upper control limit$,$ the results are inconclusive.

E$.$ The number of defects is greater than the upper control limit$,$ so it is assumed that the process is in control.