The line will become very large.
3)
3.
λ
=
15
arrivals per hour (1 arrival every 4 minutes is
60
4
=
15
per hour)
μ
=
18
inspections per hour
(a)
how many trucks would be in the system,
5
So 5 trucks in the system.
(b)
how long it would take for a truck to get through the inspection station,
1
3
of an hour – 20 minutes.
(c)
the utilization of the person staffing the station,
0.833
Working at 83.3% of capacity.
(d) the probability that there are more than three trucks in the system.
¿
0.482
There is a 48.2% chance that there will be more than 3 trucks in the system.

4.
λ
=
750
arrivals per hour
μ
=
900
fee collections per hour (4 seconds to collect one fee is
60
4
=
15
per minute &
15*60=900 per hour)
(a)
the percent of time the operator was idle,
0.1667
The operator was idle for 16.67% of the time, which is approximately
10 minutes per hour (.1667*60).
(b)
how much time you would expect it to take to arrive, pay your toll and move on,
0.007
That is 0.007 of one hour, which is 24 seconds (.007*60*60).
(c)
how many cars would be in the system,
5
5 cars would be expected to be in the system.
(d)
the probability that there would be more than four cars in the system.

¿
0.402
There is a 40.2% chance of there being more than 4 cars in the system.
5.
λ
=
10
arrivals per hour
μ
=
15
customers served per hour (1 customer per 4 minutes is
60
4
=
15
per hour)
(a)
What is the probability that the server at the window is idle?
There is a 33.3% chance that the server at the window is idle.
(b) What is the average number of cars waiting in line?
1.333
On average, there will be 1.333 cars waiting in line.
(c)
What is the average amount of time a customer spends until receiving their order?
0.200

20% of an hour. That is 12 minutes.

#### You've reached the end of your free preview.

Want to read all 6 pages?

- Spring '16
- Skordi
- average number, Mower, Jesse James, 33.3%, 16.67%