=11.8.* Newell and Jeff are the two barbers in a barber shop they own and operate. They provide two chairs for customers who are waiting to begin a haircut, so the number of customers in the shop varies between 0 and 4. For n 0, 1, 2, 3, 4, the probability Pn that exactly n customers are in the shop is P0 1

⁄16, P1 4

⁄16, P2 6

⁄16, P3 4

⁄16, P4 1

⁄16.

a. Use the formula L 0P0 1P1 2P2 3P3 4P4 to calculate L. How would you describe the meaning of L to Newell and Jeff?

b. For each of the possible values of the number of customers in the queueing system, specify how many customers are in the queue. For each of the possible numbers in the queue, multiply by its probability, and then add these products to calculate Lq. How would you describe the meaning of Lq to Newell and Jeff?

c. Given that an average of four customers per hour arrive and stay to receive a haircut, determine W and Wq. Describe these two quantities in terms meaningful to Newell and Jeff.

d. Given that Newell and Jeff are equally fast in giving haircuts, what is the average duration of a haircut?