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The weight in pounds of people in a certain population has a normal distribution, with a mean of 150 and standard deviation of 40. Of the people who weigh over 170 lbs, what percent weigh more than 200? (using conditional probability)

To do this, I calculated the probability P(x>170) ==> .3085 (using normal distribution) Using the conditional probability formula P( x>200 | x>170) = P( x>200 AND x>170) / P(x>170)

*Here it seems like P(x>200 and x>170) is equal to P(x>200) -- is this wrong to assume?

I'm not sure how to come up with P(x>200 and x>170) -- sticking to formulas, are these events dependent?

Any insights are greatly appreciated. Thanks for your time!

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P(x>200 and x>170) = P(x>200) .

I wouldn't call it an assumption. I'd call it a fact. Any x which is > 200 is necessarily greater than 170. I.e., In the event "x>200 and x>170", "and x > 170" is redundant.

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    $\begingroup$ Thank you! This is obvious, not sure why I was confused by it:) Thanks for your help $\endgroup$ – Stats_anon Jan 3 '18 at 0:24

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