# math

posted by .

automoniles arrive at the drive-through windom at a post office at the rate of 4 every 10 minutes. the average service time is 2 minutes. the poisson distributimes are exponentially distributed.

(A) what is the average time a car is in the system?

(b) what is the average number of cars in the system?

(c) what is the average time cars spend waiting to receive service?

(d) what is the average number of cars in line behind the customer receiving service?

(e) what is the probability that there are no cars at the window?

(f) what percentage of the time is the postal clerk busy?

(g) what is the probability that there are exactly 2 cars in the system?

## Similar Questions

1. ### operations management/supply chain

Suppose you are managing a service system in which customers arrive at a rate of two per minute according to a Poisson process. You are investing in a single machine that provides the service and does so with exponential service time. …
2. ### Operation Management

Customers arrive at service window every 3.6 minutes(exponentially distributed) and service time is 2.4 minutes )exponentially distributes) What is the average lenght of waiting line and waiting time?
3. ### Operations Management

Fresh Sub hires three workers during the peak hours. When customers arrive, one worker is dedicated to order taking and preparing the bread and the meat; then the customer is passed to the second worker, who asks the customer about …

Customers arrive at Paul Harrold¡¯s styling shop at a rate of 3 per hour, distributed in a Poisson fashion. Paul a perform haircuts at a rate of 5 per hour, distributed exponentially. a) Find the average number of customers waiting …
5. ### stat

The average commute time via train from the Chicago O'Hare Airport to downtown is 60 minutes with a standard deviation of 15 minutes. Assume that the commute times are normally distributed. What proportion of commutes would be: longer …
6. ### Quantative reserach

1. The average commute time via train from the Chicago O'Hare Airport to downtown is 60 minutes with a standard deviation of 15 minutes. Assume that the commute times are normally distributed. What proportion of commutes would be: …
7. ### Q Research

2. The average commute time via train from the Chicago O'Hare Airport to downtown is 60 minutes with a standard deviation of 15 minutes. Assume that the commute times are normally distributed. What proportion of commutes would be: …
8. ### Math

Suppose that the service rate to a waiting line system is 10 customers per hour (exponentially distributed). Analyze how the average waiting time is expected to change as the arrival rate varies from two to ten customers per hour (exponentially …
9. ### statistics

c. The arrival of large jobs at a computer centre forms a Poisson process with rate 2 per hour. The service time of such jobs are exponentially distributed with mean 20 minutes. Only 4 large jobs can be accommodated in the system at …
10. ### Statistics

Service times for customers at a post office follow some right-skewed distribution with mean 2.91 minutes and standard deviation 1.74 minutes. (a) Can you calculate the probability that the average service time for the next two customers …

More Similar Questions