Question: Coal is carried from a certain mine to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put up 75 tons of coal on each car. The actual weights of coal are normally distributed with mean \(\mu =75\) and \(\sigma =0.8\)

(a) What is the probability that one car chosen at random will have less than 74.5 tons of coal?

(b) What is the probability that 20 cars chosen at random will have a mean load weight that is less than 74.5?

(c) Suppose that the weight of coal in one car is less than 74.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment?. Suppose that the weight of coal in 20 cars has an average less than 74.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment?