time required for an automotive center to complete an ol change service on an au
ID: 3069690 • Letter: T
Question
time required for an automotive center to complete an ol change service on an automobile approximately follows a normal distibution, with a mean of 17 minutes and a standard deviation of 2 5 minutes (a) The automotive center guarantees customers that the service will take no longer than 20 (b) If the automotive center does not nger, the customer will receive the service for half-price What percent of customers receive the service for half-price? minutes If it does take lo want to give the discount to more than 2% or its customers, how long should it make the guaranteed time limit? (a) The percent of customers that receive the service for half-price is Round to two decimal places as needed ) (b) The guaranteed tme limit isminutes (Round up to the nearest integer as needed )Explanation / Answer
a)P(% of customers that recive the service at half price =P(X>20)=P(Z>(20-17)/2.5)
=P(Z>1.2) =11.51%
b)
for top 2 % ; critical z =2.05
therfore corresponding waiting time =mean+z*std deviation =17+2.05*2.5=22 minutes
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