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Thread: Z-score from a negative x value

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    Z-score from a negative x value




    Hello,

    I am trying to calculate the z-score for a normal random variable(x), which has a negative value.
    I know the formula. If x < 3.4 the mu is 1 and sigma is 16, then Φ is 0.15 which has a probability of .5596[NCST]
    How would I calculate x <-3.4?

    Regards,

    Bernard

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    Re: Z-score from a negative x value


    I guess you are having a normal table with positive quantiles only, similar to the below table:

    http://www.normaltable.com/

    To use the table with negative quantile, one just need to note that the standard normal distribution is symmetric about 0, i.e. we have

    \Pr\{Z \leq -x\} = \Pr\{Z \geq x\} ~~ \forall x \in \mathbb{R}

    And once you know how to calculate the probability for a complementary event, you can calculate the required probability within the precision of the given table.

  3. The Following User Says Thank You to BGM For This Useful Post:

    BernardW (11-20-2013)

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