The time required for an automotive connecter to complete an oil charge service

Question

The time required for an automotive connecter to complete an oil charge service on an automobile approximately follows a normal distribution, with a mean of 17 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 3% of its customers, how long should it make the guaranteed time limit? (a) The percent of customers that receive the service for half-price is %.

Explanation / Answer

mean = 17

standard deviation = 3

P(X>20) = 1 - P(X<20)

= 1 - P(Z < (20-mean)/standard deviation)

= 1 - P(Z<(20-17)/3)

= 1 - P(Z <1)

= 1 - 0.8413

= 0.1587

So, percent of customers that recieve service for half price = 15.87%

b) To limit to 3%, P(X<c) = 1-0.03

P(X<c) = 0.97

P(Z < (c-17)/3) = 0.97

(c-17)/3 = 1.88

c = 22.64 minutes

The guaranteed time limit should be made as 22.64 minutes

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