Coal is carried from a mine in West Virginia to a power plant inNew York in hopper cars on a long train. The automatic hopper carloader is set to put 78 tons of coal into each car. The actualweights of coal loaded into each car are normallydistributed, with mean μ = 78 tons and standarddeviation σ = 1.2 ton.
(a) What is the probability that one car chosen at random willhave less than 77.5 tons of coal? (Round your answer to fourdecimal places.)
(b) What is the probability that 21 cars chosen at random will havea mean load weight x of less than 77.5 tons of coal?(Round your answer to four decimal places.)
(c) Suppose the weight of coal in one car was less than 77.5 tons.Would that fact make you suspect that the loader had slipped out ofadjustment?
Yes No   Â
Suppose the weight of coal in 21 cars selected at random had anaverage x of less than 77.5 tons. Would that fact make yoususpect that the loader had slipped out of adjustment? Why?
Yes, the probability that this deviation is random is verysmall. Yes, the probability that this deviation is random is verylarge.    No, the probability that thisdeviation is random is very small. No, the probability that thisdeviation is random is very large.
