the time required for an automotive center to complete an oil change service on

Question

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 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 recieve the service for half-price. What percent of customers recieve 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?

Explanation / Answer

a)percent of customers recieve the service for half price =P(X>20)=P(Z>(20-15)/3)=P(Z>1.6667)=4.78%

b)for 98th percentile ; zscore =2.0537

hence corresponding time =mean+z*Std deviation =15+2.0537*3=21.16 minute

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