Question

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 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 to give the discount to more than 2​% of its​ customers, how long should it make the guaranteed time​ limit?

Answer 1

We have a normal distribution with a mean of 19 minutes and a standard deviation of 3 minutes. To solve the problem we're going to need the help of a calculator:

P(z>20) = 0.3694

Therefore, the percentage of costumbers that will receive the service for half-price is: 36.94%.

Also, we've found that p(z>25.16) = 0.02. Therefore, if they only want to offer half-price discount to only 2% of its costumber, the time limit should be 25.16 minutes.