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 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 2% of its customers, how long should it make the guaranteed time limit?
Accepted Solution
A:
Answer:We have a normal distribution with a mean of 19 minutes and a standard deviation of 3 minutes. To solve the problem we're going to need the help of a calculator:P(z>20) = 0.3694Therefore, the percentage of costumbers that will receive the service for half-price is: 36.94%.Also, we've found that p(z>25.16) = 0.02. Therefore, if they only want to offer half-price discount to only 2% of its costumber, the time limit should be 25.16 minutes.