Q$2.$ A producer of contact lenses regularly takes samples of $100$ lenses and inspects them for

scratches. If a lens has a single scratch, it cannot be sold. The results of $10$ samples $(100$

lenses in each$)$ are shown below:

a$)$ What is the average proportion defective?

b$)$ What are the lower and upper $3-$sigma control limits$?$

c$)$ Is the process out of control? If yes, which sample is out of control?