Question

Fast Auto Service provides oil and lube service for cars. It is known that the mean time taken for oil and tube service at this garage is 15 minutes per car and the standard deviation is 2.4 minutes. The management wants to promote the business by guaranteeing a maximum waiting time for its customers. If a customer's car is not serviced within that period, the customer will receive a 50% discount on the charges. 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. 9. The management of a supermarket wants to adopt a new promotional policy of giving a free gift to every customer who spends more than a certain amount per visit at this supermarket. The expectation of the management is that after this promotional policy is advertised, the expenditures for all customers at this supermarkt will be normally distributed with a mean of $110 and a standard deviation of $20. If the management wants to give free gifts to at most 10% of the customers, what should the amount be above which a customer would receive a free gift?

Answer 1

8.

Let X be the waiting time. Then X ~ N(15, 2.4)

If the company wants to limit the discount to at most 5% of the customers, the maximum guaranteed waiting time will be the 95% percentile.of the waiting time.

Z value for 95% percentile is 1.645

Maximum guaranteed waiting time = = 15 + 1.645 * 2.4 = 18.95 minutes

04月

9.

Let X be the expenditure at the supermarket. Then X ~ N(110, 20)

If the management wants to give free gifts to at most 10% of the customers, the amount will be the 90% percentile.of the expenditure at the supermarket

Z value for 90% percentile is 1.28

Minimum amount to be spent for the gift  = = 110 + 1.28 * 20 = $135.6

04月