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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?

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