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The time required for an automotive center to oil change service on an automobile approximately follows a normal? distribution, with a mean of 19 minutes 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 3?% of its? customers, how long should it make the guaranteed time? limit?
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