A state highway goesthrough a small town where the posted speed limit drops down to40MPH, but which out of town drivers don’t observe very carefully.Based on historical data, it is known that passenger car speedsgoing through the city are normally distributed with a mean of 47mph and a standard deviation of 4MPH. Truck speeds are found to benormally distributed with a mean of 45MPH and a standard deviationof 6MPH. The town installed a speed camera and wants to set athreshold for triggering the camera to issue citations. If thecamera is triggered, the driver is mailed a flat $50 ticket forcars and a flat $75 for trucks. On average 100 cars and 25 trucksgo through the city in a day.
- If the town sets the camera triggering speed at 50MPH, how muchrevenue will it make in a month (assume a month has 30 days)
- The town wants to set the triggering speed at a value such thatthe fastest 10% of truck drivers get ticketed. At what value shouldthey set the trigger?
- At this trigger value, what percentage of cars are ticketed andwhat is the monthly revenue for the city?
