The time required for an automotive center to complete an oil change service on

Question

The time required for an automotive center to complete an oil change service on an automobile approximately follows a normal distribution, with a mean of 19 minutes and a standard deviation of 4 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 5% of its customers, how long should it make the guaranteed time limit? Click the icon to view a table of areas under the normal curve (a) The percent of customers that receive the service for half-price is % (Round to two decimal places as needed.) (b) The guaranteed time limit isminutes. (Round up to the nearest minute.)

Explanation / Answer

a) Percent of customers that receive the service for half-price

= P(X < 20)

= P(z < (20 - 19)/4)

= P(z < 0.25)

= 59.87%

b) z score for 5% area to its right = 1.645

Hence,

Guaranteed time limit = 19 + 1.645*4 = 26 minutes

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