a.) The management of a supermarket wants to adopt a new promotional policy of g
ID: 3226269 • Letter: A
Question
a.) 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 supermarket will be normally distributed with a mean of $105 and a standard deviation of $17. If the management wants to give free gifts to at most 9.18% of the customers, what should the amount be above which a customer would receive a free gift?
Round your answer to two decimal places.
A customer should spend at least $_____ to receive a free gift.
b.) Fast Auto Service provides oil and lube service for cars. It is known that the mean time taken for oil and lube 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 3% 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.
Round your answer to the nearest minute.
Explanation / Answer
answer for question A
mu = the population mean = 105
sigma = population standard deviation = 17
the amount spent such that 100% - 9.18% = 90.82% of people will NOT get the free gift.
z value =1.329752=1.33
z = (x-mu)/sigma
S - 105 = 1.33 * 17
S - 105 = 22.61
S = 105 + 21.84
S = 127.61
A customer should spend at least $127.61
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