SOLUTION: 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 ca

Question 1192925: 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?
(d) Among 20 randomly chosen cars, most likely, how many cars will be loaded with less than 74.4 tons of coal? Calculate the corresponding probability.
(e) In the senior management meeting, it is discussed and agreed that a car loaded with less than 74.4 tons of coal is not cost effective. To reduce the ratio of cars to be loaded with less than 74.4 tons of coal, it is suggested changing current average loading of coal from 75 tons to a new average level, M tons. Should the new level M be (I) higher than 75 tons or (II) lower than 75 tons? (Write down your suggestion, no explanation is needed in part (e)).
Answer by ikleyn(52793) (Show Source): You can put this solution on YOUR website!
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Too many questions.

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