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Coal is carried from a mine in West Virginia to a power plant in Georgia in hopper cars on a long train. The automatic loader is set to put 75 tons of coal into each car. The actual weights of coal loaded into each car is known to follow a distribution with a mean of 75 tons and a standard deviation of 1.7 tons. In a random sample of 32 cars, you are interested in the probability that the mean of that sample is less than 74.5 tons of coal.
What is the probability that the sample mean coal weight is less than 74.5 tons?
a) 0.0244
b) 0.0485
c) 0.3860
d) 0.9756
e) None of the above are correct.
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