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According to CTG, if you have X1...Xn independent variables with same distribution (here it's N(500,80)), their mean X has a normal distribution N( µ; σ/sqrt(n))
(sorry, can't write proper math symbols in browser)
So in this case we have µ = 500, σ = 80, sqrt(n) = 10. So mean of X has the distribution of N(500;8)
Now once you have a distribution, you need to calculate
P(490 < mean X < 510)
Once you normalize, it's
P (-1.25 < Z < 1.25). That should be easy to calculate
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The Central Limit Theorem #3
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According to CTG, if you have X1...Xn independent variables with same distribution (here it's N(500,80)), their mean X has a normal distribution N( µ; σ/sqrt(n)) (sorry, can't write proper math symbols in browser) So in this case we have µ = 500, σ = 80, sqrt(n) = 10. So mean of X has the distribution of N(500;8)
Now once you have a distribution, you need to calculate P(490 < mean X < 510) Once you normalize, it's P (-1.25 < Z < 1.25). That should be easy to calculate