Flybynite Airlines has a regularly scheduled flight from Minneapolis to Frankfurt every weekday evening at 6:30. Based on a complex relationship between Flybynite and Bigrain Airlines, a local line that flys to a number of small towns, 100 seats are reserved for passengers from two of Bigrain's flights, which arrive at 5:00 p.m. each weekday. The number of passengers on the flight from Tri-mountain, Montana, has a normal distribution with a mean of 40 passengers and a variance of 100. The number of passengers on the other flight, from Bighog, Iowa, is also normally distributed with a mean of 35 passengers and a variance of 144. The numbers of passengers on these two flights have a correlation of 0.5.
a. What is the probability that all 100 seats on the Frankfurt flight will be filled?
b. What is the probability that between 75 and 90 seats will be filled?