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Math Help - continuous prob

  1. #1
    Senior Member sfspitfire23's Avatar
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    continuous prob

    I have a function f(x) where f(x)=3/8*(7-x)^2 when 5<=x<=7 and 0 otherwise.

    I calculated the E(x)=5.5
    V(x)=.15
    and Std dev=.378

    Now, I have a question asking this-
    Find an exact interval within which 80% of the pH measurements must lie with half of the other 20% of the pH measurements lying below the lower limit and the other half lying above the upper limit.

    I know this is chebychev's thm. but I have no idea how to apply it in this case
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  2. #2
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    Quote Originally Posted by sfspitfire23 View Post
    I have a function f(x) where f(x)=3/8*(7-x)^2 when 5<=x<=7 and 0 otherwise.

    I calculated the E(x)=5.5
    V(x)=.15
    and Std dev=.378

    Now, I have a question asking this-
    Find an exact interval within which 80% of the pH measurements must lie with half of the other 20% of the pH measurements lying below the lower limit and the other half lying above the upper limit.

    I know this is chebychev's thm. but I have no idea how to apply it in this case
    \int_5^a f(x) \, dx = 0.1. Solve for a.

    \int^7_b f(x) \, dx = 0.1. Solve for b.
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