Airline records show that on a certain long-haul route, luggage weight averages 17.3 kg per passenger, with a standard deviation of 3.1 kg per passenger. Passengers weight on average 70 kg with a standard deviation of 8 kg. i. determine the probability that the average luggage weight per passenger, in a queue of 25 at the baggage check-in counter will be less than 16 kg. (5 marks) ii. Determine the probability that the total weight of 400 passengers booked on 3 B74? aircraft will exceed 28,480 kg. (5 marks) iii. Determine the probability that the 400 passengers and their luggage will exceed a maximum payload requirement of 35,450 kg. Outline any assumptions made. (7.5 marks)