Along a stretch of highway the posted speed limit is 80 km/h. However, not everyone obeys the posted speed limit. The probability distribution below gives historical data for the random variable X, the maximum speed reached by a car along this highway (measured in km/h).
x 80 90 100 110 120 130
f(x) 0.65 0.16 0.08 0.06 0.03 0.02
Suppose that to use the highway drivers must pay a fee. Each car must pay a basic fee of $3, plus an additional $0.25 for every km/h over the speed limit they reach in their maximum speed. The province in charge of the highway has set up cameras along the highway to monitor who uses the highway (they can also monitor speed this way), and then sends the registered owner of the car a bill for the amount of the fee.
Find the variance for the fee.
How to solve?