The weight of students who use the main elevators varies from one student to another in accordance with the normal distribution, the mean weight being 75 kilograms (kgs) and the standard deviation of 10 kilograms.
(a) What is the probability that a randomly chosen student leaving one of the main elevators weighs at least 68 kilograms to at most 90 kilograms?
(b) Find the 80th percentile, and interpret its meaning in the context of the data.
(c) Twelve students enter one of the main elevators. Using this information, answer parts (i) and (ii):
(i) What is the probability that four of these students weigh more than 85 kilograms?
(ii) For safety purposes, the 'maximum capacity' of this elevator is stated as '13 persons, or 1000 kilograms'. What is the probability that this group of twelve students exceed the maximum weight capacity of the elevator?