The time required for an automotive center to complete an oil change service on an automobile approximately follows a normaldistribution, with a mean of 19 minutes and a standard deviation of 2 minutes.

(a) The automotive center guarantees customers that the service will take no longer than 20 minutes. If it does takelonger, the customer will receive the service forhalf-price. What percent of customers receive the service forhalf-price?

(b) If the automotive center does not want to give the discount to more than 5% of itscustomers, how long should it make the guaranteed timelimit?