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Thread: [SOLVED] Normal Distribution

  1. #1
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    [SOLVED] Normal Distribution

    Loans provided to customers of bank X follows Normal distribution with a mean of 1,500,000 crowns (czk). Given that the standard deviation is 1,000,000 czk which loan amount is such that only 10% of the loans have higher balance?
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  2. #2
    Senior Member Twig's Avatar
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    hi

    For normal distribution:

    $\displaystyle P(X\leq x)=\Phi\left(\frac{x-\mu}{\sigma}\right) $

    For 10% to be higher, we need $\displaystyle P(x\leq x)=0.9 $

    Therefore...

    $\displaystyle 0.9=\Phi\left(\frac{x-1.5}{1}\right) $

    Looking at the standard distribution table, we see that $\displaystyle 0.9 $ corresponds to approx. $\displaystyle 1.28 $

    In other words, solve $\displaystyle \frac{x-1.5}{1}=1.28 $

    Gives $\displaystyle x = 2.78 $

    So the loan is 2,780,000(czk)
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  3. #3
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    Thanks Twig
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