Question

Fast Auto Service provides oil and lube service for cars. It is known that the mean...

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 discount to at most 4% of the customers. What should the maximum guaranteed waiting time be? Assume that the times taken for oil and lube service for all cars have a normal distribution.

Round your answer to the nearest minute.

The maximum guaranteed waiting time should be approximately ?????? minutes.

Homework Answers

Answer #1

Solution:-

Given that,

mean = = 15

standard deviation = = 2.4

Using standard normal table,

P(Z < z) = 4%

= P(Z < z) = 0.04  

= P(Z < -1.75) = 0.04

z = -1.75

Using z-score formula,

x = z * +

x = -1.75 * 2.4 + 15

x = 10.8

x = 11 minutes.

The maximum guaranteed waiting time should be approximately 11 minutes.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Fast Auto Service provides oil and lube service for cars. It is known that the mean...
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...
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...
Speedy Oil provides a single-channel automobile oil change and lubrication service. Customers provide an arrival rate...
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...
“Dawit Lube” is a regional chain that provides a standard service for performing oil changes and...
“Dawit Lube” is a regional chain that provides a standard service for performing oil changes and basic checkups on automobiles. The chain has a standard that says the average time per car for this service should be 12.5 minutes. There is considerable variability in times due to differences in layout of engines, degree of time pressure from other jobs, and many other sources. As a result, the management of the chain decided to study if the standard is being met...
“Fana Lube” is a regional chain that provides a standard service for performing oil changes and...
“Fana Lube” is a regional chain that provides a standard service for performing oil changes and basic checkups on automobiles. The chain has a standard that says the average time per car for this service should be 15 minutes. There is considerable variability in times due to differences in layout of engines, degree of time pressure from other jobs, and many other sources. As a result, the management of the chain decided to study if the standard is being met...
From long term experience, it is known that the time it takes to do an oil...
From long term experience, it is known that the time it takes to do an oil change on a vehicle has a normal distribution with a mean of 17.8 minutes and a standard deviation of 5.2 minutes. An auto service shop will give a free oil change to any customer who has to wait longer than the guaranteed time it takes to complete the job. a.) If the shop guarantees the service will take 25 minutes or less, what percentage...
The time required for Quick Changers to complete an oil change service on an automobile follows...
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...
The time required for an automotive center to complete an oil change service on an automobile...
The time required for an automotive center to complete an oil change service on an automobile approximately follows a normal​ distribution, with a mean of 15 minutes and a standard deviation of 4 minutes. ​(a) The automotive center guarantees customers that the service will take no longer than 20 minutes. If it does take​ longer, the customer will receive the service for​ half-price. What percent of customers receive the service for​ half-price? ​(b) If the automotive center does not want...
Speedy Oil provides a single-server automobile oil change and lubrication service. Customers provide an arrival rate...
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...
The time required for an automotive center to complete an oil change service on an automobile...
The time required for an automotive center to complete an oil change service on an automobile approximately follows a normal​ distribution, with a mean of 19 minutes and a standard deviation of 3.5 minutes. ​(a) The automotive center guarantees customers that the service will take no longer than 20 minutes. If it does take​ longer, the customer will receive the service for​ half-price. What percent of customers receive the service for​ half-price? ​(b) If the automotive center does not want...