The time required for an automotive center to complete a 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 7% of its customers, how long should it make the guaranteed time limit?