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

Let us consider the Miles Per Gallon for customers of MallState is denoted by X. Then, X~N(34,2.5²)

We have to find the top 10%ile and which guest(s) from problem G would benefit from this program.

the top 10% of lie would-be those X above 0.9 (i.e., 100% - 90% = 10% or 1 - 0.9 = 0.1) i.e. 90th percentile. Hence, we need to find 90th percentile of the given normal distribution which is as below:

Thus, the guests whose miles per gallon value are less than 37.205 from problem G would benefit from this program.

Note: If you know R, then you can directly obtain 90th percentile as,

> qnorm(0.90,34,2.5)
[1] 37.20388