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 17 minutes and a standard deviation of 22 minutes,

(a) The automotive center guarantees customers that the service will take no longer than

20 minutes. If it does takelonger, 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 55% of itscustomers, how long should it make the guaranteed timelimit?

Explanation / Answer

Solution:-
a) P(X > 20) = P(Z > (20 - 17)/22)
= P(Z > 0.1364)
= 1 P(Z < 0.1364)
= 1 0.5557
= 0.4443

b) P(Z > (X - 17)/22) = 0.55
(X - 17)/22 = 0.1257
X = 17 + 0.1257*22
x = 19.7654
  

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