The neighborhood kids set up an outdoor lemonade stand in Maryland in February.

Question

The neighborhood kids set up an outdoor lemonade stand in Maryland in February. They are disappointed to find that their average customer arrival rate is only 1 per hour even though they are capable of serving 1 customer every 1.5 minutes.


What is the average number of customers waiting in the queue?

Select one:

a. 0.026

b. 0.0006

c. 0.038

d. 1.538

e. 1

What is the average customer waiting time in the queue?

Select one:

a. 0.0 seconds

b. 2.3 seconds

c. 40.0 seconds

d. 60.0 seconds

e. 90.0 seconds

What is the probability that the kids will have no customers in the system?

Select one:

a. 0.0%

b. 2.5%

c. 50.0%

d. 97.5%

e. 100.0%

Explanation / Answer

Arrival rate, = 1 per hour

Service rate, = 60/1.5 = 40 per hour

1) b. 0.0006

Average number of customers waiting in the queue, Lq = = 2/(*(-)) = 12/(40*(40-1)) = 0.0006

2) b. 2.3 seconds

Average customer waiting time in the queue, Wq = /(*(-)) = 1/(40*(40-1)) = 0.0006 hours = 0.0006*3600 = 2.3 sec

3) d. 97.5%

Probability of no customers in the system, P0 = 1 - / = 1 - 1/40 = 0.975

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