Seats in commercial airplanes are designed so most passengers are comfortably seated. To design an airplane, an engineer at Bombardier Aerospace uses the normally distributed height of Québec adults, which has a mean of 170 cm and a standard deviation of 12 cm a. The designer will design the seating so 98% of passengers are comfortable. What is the height of someone who is taller than 98% of all other Québec adults?
b. The airplane can hold up to 110 passengers. What is the probability that the average height of passengers is smaller than 100 or larger than 190 cm?
c. If we market this airplane to the American market for which the mean height of adult Americans is 185 cm with a standard deviations of 16 cm, what proportion of American adults would be taller than the height found in (a)? Would this be a problem for Bombardier when it tries to sell the plane to American airline companies?