The time for a Greased Lighting oil change on a car is approximately normally di

Question

The time for a Greased Lighting oil change on a car is approximately normally distributed with an average of 17 minutes and a standard deviation or 2.5 minutes.

A.) The "greasers" are working in te pits guarantee that the oil change will take no longer than 20 minutes. If it takes longer that that, a customer will only have to pay half-fare. What is the approximate percentage of customers that can expect to pay half price?

B.) If the Greases Lighting owner, Abby Egan, does not want to give this half fare price to more than 3% of its customers, how long should the company make the guarantee time limit?

Explanation / Answer

Normal Distribution
Mean ( u ) =17
Standard Deviation ( sd )=2.5
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
P(X > 20) = (20-17)/2.5
= 3/2.5 = 1.2
= P ( Z >1.2) From Standard Normal Table
= 0.1151                  
P(X < = 20) = (1 - P(X > 20)
= 1 - 0.1151 = 0.8849 ~ 88.49% are would pay half fare
b)
P ( Z > x ) = 0.03
Value of z to the cumulative probability of 0.03 from normal table is 1.88
P( x-u/ (s.d) > x - 17/2.5) = 0.03
That is, ( x - 17/2.5) = 1.88
--> x = 1.88 * 2.5+17 = 21.7025

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