In: Statistics and Probability
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 15 minutes and a standard deviation of 4 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?