The cardboard bales produced at a local recycling depot have an average weight of 400kg with a standard deviation of 50kg.
(a) Assume that the bale weights follow a normal model
(i) What percentage of the bales weighs between 380 kg and 420 kg?
(ii) What is the probability that the mean weight of 8 randomly sampled bales is between 380 kg and 420 kg
(iii) A Random sample of 40 bales is loaded onto a truck that has a 16500kg load limit. What is the probability that the truck is overloaded?
(b) If we cannot assume that the individual bale weights follow a normal model, are any of the probability calculations in part a) still valid? Explain your answer.