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Math Help - If P(0<z<a)=0.3907, find a

  1. #1
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    If P(0<z<a)=0.3907, find a

    If P(0<z<a)=0.3907, find a.

    Can anyone help me solve this? I have one of those charts.

    Im looking in my book over and over, but it simply does not explain how to solve a problem like this anywhere.

    I have no idea what the first step is, and I would like a simple explanation on how to find the answer, which is 1.23(z score)
    Last edited by mr fantastic; March 24th 2011 at 06:18 PM. Reason: Copied title into main body of post.
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  2. #2
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    Quote Originally Posted by NecroWinter View Post
    If P(0<z<a)=0.3907, find a.

    Can anyone help me solve this? I have one of those charts.

    Im looking in my book over and over, but it simply does not explain how to solve a problem like this anywhere.

    I have no idea what the first step is, and I would like a simple explanation on how to find the answer, which is 1.23(z score)
    Note that Pr(0 < Z < a) = Pr(Z < a) - Pr(Z < 0) = Pr(Z < a) - 0.5.

    So solve Pr(Z < a) = 0.8907 for a.
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    Note that Pr(0 < Z < a) = Pr(Z < a) - Pr(Z < 0) = Pr(Z < a) - 0.5.

    So solve Pr(Z < a) = 0.8907 for a.
    How did you know that P(Z<a) = .8907 ?

    Sorry, I just dont have a very good book here and im fairly lost.

    the z score 1.23 is supposed to be the final answer
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  4. #4
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    Quote Originally Posted by NecroWinter View Post
    How did you know that P(Z<a) = .8907 ?

    [snip]
    Read the first line of what I posted!
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  5. #5
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    It was explained that

    \displaystyle P(0 < Z < a) = P(Z < a) - P(Z < 0) = Pr(Z < a) - 0.5

    Does this make sense to you?
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  6. #6
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    Yes, I get it now. 0 is in the middle, and is 50%.

    But if I can follow up on this type of question, what if you only have variables? How would you be able to solve a problem like this?

    For example: P(-b<z<b)=.8664 (find b)

    theres gotta be a general rule of thumb here. Hopefully im not asking too many questions but Id like to understand whats happening here, and im not sure what to call these kinds of problems so I had to use the problem in the subject
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  7. #7
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    You can say that \displaystyle P(-b<Z<b)=2\times P(0<Z<b) = 0.8664\implies P(0<Z<b) = \frac{0.8664}{2}
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  8. #8
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    well thats certainly an interesting trick you showed me there, pickslides. It will be very helpful!

    Thanks to both of you
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