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 a customer waits 2 minutes or more in the line?

a.

0.4615

b.

0.6345

c.

0.5385

d.

0.3655

question 2:

Tourists stop at an information desk at a rate of one every 30 minutes, and answering their questions takes an average of 15 minutes each. There are 8 employees on duty. If a tourist isn't served immediately, how long on average would the tourist have to wait for service?

a.

0.667 minutes

b.

0.333 minutes

c.

0.047 minutes

d.

0.833 minutes

question 3

During the early morning hours, customers arrive at a branch post office at an average rate of 45 per hour (Poisson), while clerks can handle transactions in an average time (exponential) of 4 minutes each. Find the minimum number of clerks needed to keep the average time in the system to under 5 minutes.

Select one:

a.

6

b.

7

c.

4

d.

5