Question

Speedy Oil provides a single-channel automobile oil change and lubrication service. Customers provide an arrival rate of 2.5 cars per hour. A mechanic needs 15 minutes to serve one car. Assume Poisson arrivals and exponential service time (show steps)

A) What is the average number of cars in the system (auto shop)

B) What is the probability that an arrival has to wait for service

C) What is the average time that a car waits for the oil and lubrication

D) What is the average time a car spends in the auto shop

Answer #1

Speedy Oil provides a single-server automobile oil change and
lubrication service. Customers provide an arrival rate of 4 cars
per hour. The service rate is 5 cars per hour. Assume that arrivals
follow a Poisson probability distribution and that service times
follow an exponential probability distribution.
A) What is the average number of cars in the system? If
required, round your answer to two decimal places
L =
B) What is the average time that a car waits for the...

Exercise 11.2.5 Customers arrive at Bunkey’s car wash service at
a rate of one every 20 minutes and the average time it takes for a
car to proceed through their single wash station is 8 minutes.
Answer the following questions under the assumption of Poisson
arrivals and exponential service.
(a) What is the probability that an arriving customer will have
to wait?
(b) What is the average number of cars waiting to begin their
wash?
(c) What is the probability...

Fast Auto Service provides oil and lube service for cars. It is
known that the mean time taken for oil and lube service at this
garage is 15 minutes per car and the standard deviation is 2.4
minutes. The management wants to promote the business by
guaranteeing a maximum waiting time for its customers. If a
customer's car is not serviced within that period, the customer
will receive a 50 % discount on the charges. The company wants to
limit...

Fast Auto Service provides oil and lube service for cars. It is
known that the mean time taken for oil and lube service at this
garage is 15 minutes per car and the standard deviation is 2.4
minutes. The management wants to promote the business by
guaranteeing a maximum waiting time for its customers. If a
customer's car is not serviced within that period, the customer
will receive a 50% discount on the charges. The company wants to
limit this...

Fast Auto Service provides oil and lube service for cars. It is
known that the mean time taken for oil and lube service at this
garage is 15 minutes per car and the standard deviation is 2.4
minutes. The management wants to promote the business by
guaranteeing a maximum waiting time for its customers. If a
customer's car is not serviced within that period, the customer
will receive a 50% discount on the charges. The company wants to
limit this...

Question 2
A fast-food franchise is considering
operating a drive-up window food-service operation. Assume that
customer arrivals follow a Poisson probability distribution, with
an arrival rate of 24 cars per hour, and that service times follow
an exponential probability distribution. Arriving customers place
orders at an intercom station at the back of the parking lot and
then drive to the service window to pay for and receive their
orders. The following three service alternatives are being
considered:
A single-channel operation...

In a car pressure wash the average arrival rate is 12 cars per
hour and are serviced at an average rate of 15 cars per hour, with
service times exponential.
It is requested:
a) Probability that the system is empty.
b) Average number of clients in the washing system.
c) Average number of clients in the row.
d) Average time a customer waits in line.
e) Probability of having a row of more than 2 clients.
f) Probability of waiting...

The time required for Quick Changers to complete an oil change
service on an automobile follows a normal distribution, with a mean
of 17 minutes and a standard deviation of 2.5 minutes. Quick
Changers guarantees customers that the service will take no longer
than 20 minutes, else the service is half-price. What percent of
customers receive the service for half-price? (Write your answer as
a percent, rounded to the nearest tenth of a percent.)
The time required for Quick Changers...

Marty's Barber Shop has one barber. Customers have an arrival
rate of 2.3 customers per hour, and haircuts are given with a
service rate of 4 per hour. Use the Poisson arrivals and
exponential service times model to answer the following
questions:
What is the probability that no units are in the system? If
required, round your answer to four decimal places.
P0 = _____
What is the probability that one customer is receiving a haircut
and no one is...

PLEASE ANSWER ALL question
Suppose you are the manager of Speedy Oil Change which claims
that it will change the oil in customers’ cars in less than 30
minutes on average. Further suppose that several complaints have
been filed from customers stating that their oil change took longer
than 30 minutes. Upper-level management at Speedy Oil Change
headquarters has requested that you investigate the complaints. To
begin your investigation, you randomly audit 36 oil changes
performed by Speedy Oil Change...

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