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 2.5minutes. ​(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 a discount to more than 5​% of its​ customers, how long should it make the guaranteed time​ limit? ​(a) The percent of customers that receive the service for​ half-price is which ​%. ?​(Round to two decimal places as​ needed.)

Question
Asked Oct 25, 2019
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 2.5minutes.
 
​(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 a discount to more than 5​% of its​ customers, how long should it make the guaranteed time​ limit?
 
​(a) The percent of customers that receive the service for​ half-price is which ​%. ?
​(Round to two decimal places as​ needed.)
check_circleExpert Solution
Step 1

According to the question the time required for an automotive center to complete an oil change service on an automobile approximately follows a normal​distribution, with:

μ = 17

σ = 2.5

a)

In this case, ...

P(X 20) P(X-j>20-17)
20 17
= P
2.5
X-
Z =
Then
=P(Z >1.2)
(Use standard normal table)
0.1151
Therefore, around 11.5% of customers that received the service for half-price
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P(X 20) P(X-j>20-17) 20 17 = P 2.5 X- Z = Then =P(Z >1.2) (Use standard normal table) 0.1151 Therefore, around 11.5% of customers that received the service for half-price

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