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We are given normally distributed body weights with a mean of $195$ lbs. and a standard deviation of $24$ lbs. If an elevator in town has a maximum capacity of $20$ persons and a rated maximum weight of $4100$ lbs., what is the probability that the elevator, when filled to capacity, will not exceed its rated weight? (in other words, what is the probability that a sample of $20$ citizens will have a mean weight of less than $205$ lbs.?)

This is how I thought the problem was to be worked

$$205-195=24/\sqrt{20}=1.862$$ which of course is not correct.

Jimmy R.
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barb
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  • You've correctly calculated the appropriate Z-score, all you need to do is turn that into a probability, knowing that that Z-score is distributed as a standard normal variable. – ConMan Oct 23 '14 at 23:09

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