Question

Overall, the Miles Per Gallon for customers of MallState is normally distributed around 34 MPG with a standard deviation of 2.5 MPG.

In looking to reward environmentally friendly drivers, the insurer decides to reward drivers whose cars rank in the top 10%ile of MPG. What is the top 10%ile and which guest(s) from problem G would benefit from this program?

Answer 1

This is a normal distribution question with

Given in the question
P(X < x) = 0.9
This implies that
P(Z < 1.2816) = 0.9
With the help of formula for z, we can say that
\\ x = \mu + z\sigma
\\\implies x = 34.0 + (1.2816)2.5
x = 37.2039
PS: you have to refer z score table to find the final probabilities.

All drivers who were driving with more than 37.2039 MPG, would benefit from this program
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