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Math Help - Normal Question

  1. #1
    Super Member craig's Avatar
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    Normal Question

    Hi, just doing a past paper and came across this question on the normal distributions that I'm not too sure about.

    Z - N(0,1), find z such that P(|Z| < z) = 0.790

    Normally I'd have no problem using the inverse normal function in my tables, not I'm not sure what that modulus sign does to the question?

    Thanks
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  2. #2
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    It means that you need to find the value of z such that the Probability that -z<Z<z = 0.790

    {So the bounds ( endpoints of the given interval) are symmetric}


    I think you can proceed from here.
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  3. #3
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    Quote Originally Posted by craig View Post
    Hi, just doing a past paper and came across this question on the normal distributions that I'm not too sure about.

    Z - N(0,1), find z such that P(|Z| < z) = 0.790

    Normally I'd have no problem using the inverse normal function in my tables, not I'm not sure what that modulus sign does to the question?

    Thanks
    \Pr(-z < Z < z) = 0.790. I suggest using symmetry to do the calculation.
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  4. #4
    Super Member craig's Avatar
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    Thanks for the answers.

    If P(-z < Z < z) = 0.790, then it follows that P(Z < -z) = \frac{1-0.790}{2} = 0.105.

    Using tables this gives 1.2536.

    Thanks again for the help
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