A single server queuing system with a Poisson arrival rate and exponential service time has an average arrival rate of 13 customers per hour and an average service rate of 16 customers per hour. The probability of 5 customers in the system is :

a.

0.1875

b.

0.06639

c.

0.9336

d.

0.6459

During the early morning hours, customers arrive at a branch post office at an average rate of 57 per hour (Poisson), while clerks can provide services at a rate of 19 per hour. If clerk cost is $50.96 per hour and customer waiting time represents a cost of $49 per hour, how many clerks can be justified on a cost basis

a.

4

b.

6

c.

7

d.

5

e.

8

Customers arrive at a video rental desk at the rate of 10 per minute(Poisson).Each server can handle 2.96 customers per minute(Poisson). If there are 4 servers, determine the average time it takes to rent a video tape.

a.

3.69 minutes

b.

0.424 minutes

c.

0.707 minutes

d.

0.369 minutes

A single server queuing system with a Poisson arrival rate and exponential service time has an average arrival rate of 6 customers per hour and an average service rate of 13 customers per hour. What is the probability that this system will contain 4 or more customers?

a.

0.9546

b.

0.9791

c.

0.04538

d.

0.9017