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 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 22% of its customers, how long should it make the guaranteed time limit?

Answer the questions below. Show all work please.

(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 is __ minutes? (Round up to the nearest integer as needed.)

Explanation / Answer

answer

P(X>x) = .03

P(X<x) = .97

Reading the table, if p=.97 then z = 1.88

x = mean + z (stdev)
x = 19 +1.88(3) = 19+ 5.64 = 24.64 minutes

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.