When I use my electronic cruise control, I set the speed for 70 MPH. The manufacturer says that the electronic cruise control's ability to maintain any speed is better than that of an individual driver. Under electronic cruise control, speeds are normally distributed around the set speed with a standard deviation of only 1.25 MPH.
g. Assume that the New York State Police give speeding tickets if they observe someone going faster than 73 MPH. If I am traveling home under cruise control with a set speed of 70 MPH (standard deviation of 1.25 MPH) and go through a speed trap, what is the probability that I will get a ticket?
h. When I use my electronic cruise control, what should my maximum speed be if I am willing to risk no more than a 5% chance of getting a ticket? (Assume a 1.25 MPH standard deviation).