SOLUTION: Assume that the weight of all employees who work on the forty-first floor of a city skyscraper is Normally distributed with a mean of 180 pounds and a standard deviation of 30 poun

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Question 1006518: Assume that the weight of all employees who work on the forty-first floor of a city skyscraper is Normally distributed with a mean of 180 pounds and a standard deviation of 30 pounds. What is the probability that the total weight of 9 of these workers who get on the elevator at the same time will exceed the capacity of 1800 pounds (that is, the average weight of the nine is more than 200 pounds)? [Hint: This is a sampling distribution question.]
Answer by stanbon(75887) About Me  (Show Source):
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Assume that the weight of all employees who work on the forty-first floor of a city skyscraper is Normally distributed with a mean of 180 pounds and a standard deviation of 30 pounds. What is the probability that the total weight of 9 of these workers who get on the elevator at the same time will exceed the capacity of 1800 pounds (that is, the average weight of the nine is more than 200 pounds)? [Hint: This is a sampling distribution question.]
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z(200) = (200-180)/(30/sqrt(9)) = 20/10 = 2
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P(x-bar > 200) = P(z > 2) = 0.0228
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Cheers,
Stan H.
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