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Thread: [SOLVED] Normal Distrubtion Question

  1. #1
    Member looi76's Avatar
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    [SOLVED] Normal Distrubtion Question

    Question:
    Given that $\displaystyle X \sim N(44,25)$, find $\displaystyle t$ correct to 2 decimal places when
    $\displaystyle P(X \geq t)=0.7704$

    Attempt:

    $\displaystyle = P(X \geq t)=0.7704$

    $\displaystyle \mu = 44$ , $\displaystyle \sigma^2 = 25 $, $\displaystyle \sigma= 5$

    $\displaystyle = P(\frac{X-\mu }{ \sigma } \geq \frac{X-44}{ 5})$

    $\displaystyle 1 - \frac{X-44}{5} = 0.7704$

    $\displaystyle 1 - 0.7704 = \frac{X-44}{5}$

    $\displaystyle 0.26 = \frac{X-44}{5}$

    $\displaystyle 1.3 = X - 44$

    $\displaystyle X = 45.3$

    Where did I go wrong?
    Last edited by looi76; Apr 16th 2008 at 03:46 AM.
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  2. #2
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    Quote Originally Posted by looi76 View Post
    Question:
    Given that $\displaystyle X \sim N(44,25)$, find $\displaystyle s$,$\displaystyle t$,$\displaystyle u$, and $\displaystyle v$ correct to 2 decimal places when
    $\displaystyle P(X \geq t)=0.7704$

    Attempt:
    $\displaystyle = P(\frac{X-\mu }{ \sigma } \geq \frac{X-44}{ 5})$

    $\displaystyle 1 - \frac{X-44}{5} = 0.7704$
    This is the problem here. You need to use a normal probability table to find that
    $\displaystyle \Pr(Z \geq -0.74) = 0.7704$

    Then we have:
    $\displaystyle
    -0.74 = \frac{t-44}{5}
    \Rightarrow t = 40.3$
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