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Math Help - Normal distribution, finding a value question!

  1. #1
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    Normal distribution, finding a value question!

    For a normal distribution, with a mean of 10.5 and a variance of 16.7, determine the value of X_{0} so that P(10.5 < x < X_{0}) = 0.4987.

    I am very lost on this question, any and all help is greatly appreciated!

    Answer is supposedly X_{0}=22.76
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  2. #2
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    Re: Normal distribution, finding a value question!

    Apply the fact that P(10.5 < x < X_{0}) = P(x < X_{0}) - P(x<10.5 )
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    Re: Normal distribution, finding a value question!

    Quote Originally Posted by pickslides View Post
    Apply the fact that P(10.5 < x < X_{0}) = P(x < X_{0}) - P(x<10.5 )
    0.4987 = P(x < X_{0}) - 0.5

    0.9987 = P(x < X_{0})

    Is that correct so far? Not sure what I do next
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  4. #4
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    Re: Normal distribution, finding a value question!

    Looks great

    0.9987 = P(x < X_{0})

    \displaystyle 0.9987 = P\left(z < \frac{X_{0}-10.5}{16.7}\right)

    Using the Normal Distribution Table

    \displaystyle  3.1 =  \frac{X_{0}-10.5}{16.7}
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