Fast Auto service provides oil and lube for cars. It is known that the mean time

Question

Fast Auto service provides oil and lube for cars. It is known that the mean time taken for oil and lube service at this garage is 15 minutes per car with a standard deviation of 2.4 minutes. The management wants to promote the business guaranteeing a maximum waiting time for customers. If a customer's car is not served with that period, the customers will receive a 50% discount on the charge. The company wants to limit this discount to at most 5% of the customers. What should the maximum guaranteed waiting time be? Assume that the times taken for oil and lube service for all cars have a normal distribution.

Explanation / Answer

Fast Auto service provides oil and lube for cars. It is known that the mean time taken for oil and lube service at this garage is 15 minutes per car with a standard deviation of 2.4 minutes. The management wants to promote the business guaranteeing a maximum waiting time for customers. If a customer's car is not served with that period, the customers will receive a 50% discount on the charge. The company wants to limit this discount to at most 5% of the customers. What should the maximum guaranteed waiting time be? Assume that the times taken for oil and lube service for all cars have a normal distribution.

Z value for top 5% =1.645

X= mean+z*sd = 15+1.645*2.4 = 18.948

maximum guaranteed waiting time = 18.948 minutes

or    18.95 minutes ( 2 decimals)

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