On a Certain Stretch of Highway, to Be Pulled Over $$f ( x ) = \left\{ \begin{array} { l l } \frac { 2 x ^ { 2 } - 2 x } { 219 } & 5 < x < 8 \\0 & \text { else }\end{array} \right.$$

Short Answer

On a certain stretch of highway, to be pulled over by police, the speed at which a car must travel over the speed limit of 60mph is a random variable which has the following probability density function: $$f ( x ) = \left\{ \begin{array} { l l } \frac { 2 x ^ { 2 } - 2 x } { 219 } & 5 < x < 8 \\0 & \text { else }\end{array} \right.$$
(a) Find the maximum speed at which a vehicle can go and be 90% sure that it will not be pulled over.
(b) Suppose Mary-Sue gets pulled over on this highway. What was the expected speed she was driving?