Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put 75 tons of coal into each car. The actual weight of coal loaded into each car is normally distributed, with mean of 75 tons and standard deviation of 0.8 ton. (a) There are 97% of the cars will be loaded with more than K tons of coal. What is the value of K? (b) What is the probability that one car chosen at random will have less than 74.4 tons of coal? (c) Among 20 randomly chosen cars, what is the probability that more than 2 cars will be loaded with less than 74.4 tons of coal?

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