Coal is carried from a mine 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 weights of coal loaded into each car are normally distributed with mean = 75 tons. A random sample of 9 cars is selected for inspection. The sample mean and standard deviation are 74.5 tons and 0.8 ton. What is the probability that 9 cars chosen at random will have a total load weight of less than 670.5 tons of coal?
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