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

Please hit thumps up if the answer helped you

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