Question 655726: The mean weight of loads of coal placed in train cars by a loading machine is 43.0 tons with a standard deviation of 8.0 tons. Assuming that the weight of loads placed in the train cars by this loader are normally distributed, if a random sample of 9 loads is chosen for a weight check, find the probability that the mean weight of those loads is more than 40.60 tons.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The mean weight of loads of coal placed in train cars by a loading machine is 43.0 tons with a standard deviation of 8.0 tons. Assuming that the weight of loads placed in the train cars by this loader are normally distributed, if a random sample of 9 loads is chosen for a weight check, find the probability that the mean weight of those loads is more than 40.60 tons.
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mean of the sample means: 43 tons
std of the sample means: 8/sqrt(9) = 8/3
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t(40.6) = (40.6-43)/(8/3) = -0.9
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P(x-bar > 40.6) = P(t > -0.9 when df = 8) = tcdf(-0.9,100,8) = 0.8028
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Cheers,
Stan H.
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