Question

A state highway goes through a small town where the posted speed limit drops down to 40MPH, but which out of town drivers don’t observe very carefully. Based on historical data, it is known that passenger car speeds going through the city are normally distributed with a mean of 47 mph and a standard deviation of 4MPH. Truck speeds are found to be normally distributed with a mean of 45MPH and a standard deviation of 6MPH. The town installed a speed camera and wants to set a threshold for triggering the camera to issue citations. If the camera is triggered, the driver is mailed a flat $50 ticket for cars and a flat $75 for trucks. On average 100 cars and 25 trucks go through the city in a day.

a. If the town sets the camera triggering speed at 50MPH, how much revenue will it make in a month (assume a month has 30 days)

b. The town wants to set the triggering speed at a value such that the fastest 10% of truck drivers get ticketed. At what value should they set the trigger?

c. At this trigger value, what percentage of cars are ticketed and what is the monthly revenue for the city?

Answer 1

It is known that passenger car speeds going through the city are normally distributed with a mean of 47 mph and a standard deviation of 4 MPH. Thus, . Also,

Truck speeds are found to be normally distributed with a mean of 45 MPH and a standard deviation of 6 MPH.

Thus, .

a) The probability that a car triggers a camera is

The probability that a truck triggers a camera is

That is of cars and   of trucks will be penalized.

The revenue in 1 month (30 days) is

b) Let be the triggering speed. Then,

c) The percentage of cars are ticketed is

Thus, cars are ticketed.

The new revenue in 1 month (30 days) is