A traffic engineer is studying a stretch of road on a rural highway. At his observation point, an average of 12 vehicles per hour pass. The vehicles are independent of each other.
1. What is the probability that fewer than 5 vehicles pass between 10:15 am and 10:45 am? State the distribution and parameters that you are using.
2. A vehicle passed by at 11:03 am. What is the probability that the engineer has to wait until after 11:10 am for the next vehicle to pass by? State the distribution and parameters you are using.
3. A vehicle passed and the engineer has already been waiting for 5 min for the next vehicle. What is the probability that he will wait between 7 and 10 min total for the next vehicle?
4. A traffic intern has a shift on Friday counting vehicles at the observation point between 1:00 pm and 3:00 pm. The intern counted 20 vehicles, but did not record the time at which they passed. What is the probability that 5 cars passed the observation point during the first 20 minutes of the intern's shift?
5. In order to entice the intern to work on a Sunday, his boss has offered to pay the intern a bonus of$0.75 for the first 10 vehicles he observed and $1.25 for the rest of the vehicles he observes in his 2 hour shift. What doe the intern expect to earn in bonus pay for this Sunday shift?