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 17minutes and a standard deviation of 2.5 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 5​% of its​ customers, how long should it make the guaranteed time​ limit?

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