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Math Help - Find Xₒ where P(X ≥Xₒ) = 0.65 and X ~ N(200,15)

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    Question Find Xₒ where P(X ≥Xₒ) = 0.65 and X ~ N(200,15)

    I'm currently taking Statistics 1 and I'm stuck on a problem that I've been trying to solve out for a while...hopefully one of you guys can help me out...heres the question:
    Find Xwhere P(X ≥X) = 0.65 and X ~ N(200,15)

    -From population draw a sample of 36 units. Find P(x-bar ≥ 225)
    -Construct a confidence interval at 95% confidence
    -Interpret the interval ask that on the physics forum

    please show work so i can follow & understand
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    MHF Contributor matheagle's Avatar
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    First of all, is 15 the variance or st deviation? I guess its the st deviation since it's not a perfect square.

    .65=P( X>x_0 )=P\left(Z>{x_0-200\over 15}\right)

    Next look up the 65 LOWER percentile, z0 of a st normal and solve for x0 ...

    z_0={x_0-200\over 15}
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    Quote Originally Posted by matheagle View Post
    First of all, is 15 the variance or st deviation? I guess its the st deviation since it's not a perfect square.

    .65=P( X>x_0 )=P\left(Z>{x_0-200\over 15}\right)

    Next look up the 65 LOWER percentile, z0 of a st normal and solve for x0 ...

    z_0={x_0-200\over 15}

    sorry i still don't understand, could u plz explain.
    thankx
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  4. #4
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    Quote Originally Posted by desiclub07 View Post
    I'm currently taking Statistics 1 and I'm stuck on a problem that I've been trying to solve out for a while...hopefully one of you guys can help me out...heres the question:
    Find Xwhere P(X ≥X) = 0.65 and X ~ N(200,15)

    [snip]
    Use tables or whatever way you've been taught to get the number z_0 such that \Pr(Z \geq z_0) = 0.65 where Z is the standard normal random variable.

    Substitute into z_0 = \frac{x_0 - 200}{15} and solve for x_0.

    Note: \Pr(Z \geq z_0) = 0.65 \Rightarrow \Pr(Z < z_0) = 0.35 \Rightarrow \Pr(Z > -z_0) = 0.35 \Rightarrow \Pr(Z \leq -z_0) = 0.65. Therefore -z_0 = ..... \Rightarrow z_0 = .....
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