7.2.51 The time required for an automotive center to complete an oil change serv

Question

7.2.51 The time required for an automotive center to complete an oil change service on an automobile approximately folows a normal distribution, with a mean of 19 minutes and a standard deviation of 2.5 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 2% of its customers, how long should it make the guaranteed time limit? (a) The percent of customers that receve the service for half-price is 34.46 %. Round to two decimal places as needed.) (b) The guaranteed time limit is 21 minutes. Round up to the nearest minute.)

Explanation / Answer

solution:-
b. given that 2% is 0.02
given that p = 0.02 then z = 2.0537
formula = x = z(s.d) + mean
x = 2.0537(2.5) + 19
x = 24

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