Question 102623: Here is my difficult question using probability statistics. Suppose weights in pounds of workers at a large office building can be modeled by a N(165,30) distribution. The elevator capacity is 1800 pounds. What's the probability that the total weight of 10 randomly selected workers would exceed this capacity?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Here is my difficult question using probability statistics. Suppose weights in pounds of workers at a large office building can be modeled by a N(165,30) distribution. The elevator capacity is 1800 pounds. What's the probability that the total weight of 10 randomly selected workers would exceed this capacity?
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If the population distribution is N(165,30)
the distribution means of samples of size 10 is
N(165,30/sqrt10)
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For the group to exceed 1800 lbs the average would have to exceed 180 lbs.
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P(mean > 180) = normalcdf(180,1000,165,30/sqrt(10)) = 0.057
Comment: I am using TI calculator which has the normalcdf function.
If you do not have this you would need a z-score for 180:
z(180) = (180-165)/[30/sqrt(10)] = 1.581
Then P(z>1.581) can be looked up on a z chart to give you 0.057
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Cheers,
Stan H.
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