An airport has two runways, one is North-South (N-S), and the other is East-West (E-W). Because of the prevailing winds, the E-W runway is used 80% of the days, and the N-S the remainder of the time. The selection of the runway for a given day is based on wind at the beginning of the day, and once selected will not be changed for the entire day. The airport has a single peak period each day; this is the hour between 4:00 and 5:00pm. During this peak hour, the volume of air traffic varies day to day and may be described with the normal variate N(100,10). The N-S runway is considered overcrowded of more than 125 planes use it during this period, whereas the E-W runway is considered overcrowded if more than 100 planes use it during a peak period.
a. What is the probability that the N-S runway is going to be overcrowded on a given day, if at the beginning of the day the runway is selected to be used?
b. What would be the probability of overcrowding, if at the beginning of a given day the E-W runway were selected to be used?
c. What is the probability of overcrowding at the airport, if there is no advance information as to which runway will be used on a given day?