The distribution function F(z) =

{0 if z< 5

{z/10 if 5 <= z < 8

{1-e^(-z/8) if 8 <= z

is associated with the MPG of a car. Using the Strong Law of Large Numbers, what may be the MPG?

Where should I start this problem and how would I go about using the Strong Law of Large Numbers? Would the expected cost be E(|z-beta|)? Any help would be appreciated