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Thread: Density curve

  1. #1
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    Density curve

    Density curve-6.jpg

    =1/2xbasexheight

    cannot work it out??? tried so many time
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  2. #2
    MHF Contributor
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    Re: Density curve

    For the full triangle:
    $\dfrac{1}{2}b\cdot h = 1$
    $\dfrac{1}{2}(50-17)h = 1$
    $h = \dfrac{2}{50-17}$

    That is the height at 17. So, now you have a line from $(17,h)$ to $(50,0)$. Find the equation for that line and plug in 20 to determine the height at 20. Then, you want to find area again.

    $y - y_1 = m(x-x_1)$

    $y-0 = \dfrac{0-h}{50-17}(x-50)$

    $y = \dfrac{-\dfrac{2}{50-17}}{50-17}(x-50) = -\dfrac{2}{(50-17)^2}(x-50)$

    Plug in 20 to get the height at 20.

    $y = \dfrac{60}{(50-17)^2}$

    Now, calculate area:

    $A = \dfrac{1}{2}b\cdot h = \dfrac{1}{2}(50-20)\cdot \dfrac{60}{(50-17)^2} = \dfrac{100}{121}$

    That's your probability of $X\ge 20$.

    To find $P(X<20)$, you need $1-\dfrac{100}{121} = \dfrac{21}{121}$
    Thanks from HallsofIvy
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