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 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?

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 15 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?