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Math Help - normal distribution

  1. #1
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    normal distribution

    hi could someone please help me with this question:

    Q) Y~N(50,sigma^2), P(Y>40)=0.6554, find sigma.

    I have a rough idea of how to do it and i know the answer is sigma=25 but i cannot get to this answer just wondering if someone could please break it down for me so i can see where i am going wrong.

    thanks
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  2. #2
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    Quote Originally Posted by wahhdoe View Post
    hi could someone please help me with this question:

    Q) Y~N(50,sigma^2), P(Y>40)=0.6554, find sigma.

    I have a rough idea of how to do it and i know the answer is sigma=25 but i cannot get to this answer just wondering if someone could please break it down for me so i can see where i am going wrong.

    thanks
    Get the z-value z* such that \Pr(Z > z*) = 0.6554 (you should have been taught how to do this). Note that z* < 0 (why is this obvious?).

    Then \displaystyle z* = \frac{40 - 50}{\sigma}. Solve for \sigma.
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  3. #3
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    thats what ive tried but this gives me z*=0.4 is there something i have done wrong there because then i would solve sigma=-25 when the answer is +25??
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    Quote Originally Posted by wahhdoe View Post
    thats what ive tried but this gives me z*=0.4 is there something i have done wrong there because then i would solve sigma=-25 when the answer is +25??
    If you read my first reply, you will see that I even went to the trouble of warning you that z* < 0. Is your value of z* less than zero?
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    no my value of z*=0.4
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  6. #6
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    Quote Originally Posted by wahhdoe View Post
    no my value of z*=0.4
    I can see that. But what I'm telling you is that your value is wrong. How can z* possibly be greater than zero when the value for Y is less than the mean?!

    You have made a mistake. Unless you accept this fact and then show your working on how you got this incorrect value, I have nothing more to say.
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