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Thread: [SOLVED] Normal Distrubtion Question

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

    Question:
    $\displaystyle X$ has a normal distribution, and $\displaystyle P( X > 73.05 = 0.0289 )$. Give that the variance of the distribution is $\displaystyle 18$, find the mean.

    Attempt:

    $\displaystyle = 1 - 0.0289$
    $\displaystyle = 0.9711$
    $\displaystyle = -1.897$

    $\displaystyle \sigma^2 = 18$ , $\displaystyle \sigma = 3\sqrt2$

    $\displaystyle P\left( \frac{X - \mu}{\sigma} > 73.05 \right) = -1.897$

    Don't know how to find the mean...
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by looi76 View Post
    Question:
    $\displaystyle X$ has a normal distribution, and $\displaystyle P( X > 73.05 = 0.0289 )$. Give that the variance of the distribution is $\displaystyle 18$, find the mean.

    Attempt:

    $\displaystyle = 1 - 0.0289$
    $\displaystyle = 0.9711$
    $\displaystyle = -1.897$

    $\displaystyle \sigma^2 = 18$ , $\displaystyle \sigma = 3\sqrt2$

    $\displaystyle P\left( \frac{X - \mu}{\sigma} > 73.05 \right) = -1.897$

    Don't know how to find the mean...

    The z-score corresponding to a cumulative standard normal probability of $\displaystyle 0.9711$ is $\displaystyle 1.897$.

    So:

    $\displaystyle
    \frac{73.05-\mu}{\sqrt{18}}=1.897
    $

    Now solve for $\displaystyle \mu$.

    RonL
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  3. #3
    Flow Master
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    Quote Originally Posted by looi76 View Post
    Question:
    $\displaystyle X$ has a normal distribution, and $\displaystyle P( X > 73.05 = 0.0289 )$. Give that the variance of the distribution is $\displaystyle 18$, find the mean.

    Attempt:

    $\displaystyle = 1 - 0.0289$
    $\displaystyle = 0.9711$
    $\displaystyle = -1.897$

    $\displaystyle \sigma^2 = 18$ , $\displaystyle \sigma = 3\sqrt2$

    $\displaystyle P\left( \frac{X - \mu}{\sigma} > 73.05 \right) = -1.897$

    Don't know how to find the mean...
    A question of similar ilk that might be of interest: http://www.mathhelpforum.com/math-he...n-problem.html
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