+ Reply to Thread
Results 1 to 2 of 2

Thread: Z-score from a negative x value

  1. #1
    Points: 59, Level: 1
    Level completed: 18%, Points required for next Level: 41

    Thanked 0 Times in 0 Posts

    Z-score from a negative x value


    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?



  2. #2
    TS Contributor
    Points: 22,410, Level: 93
    Level completed: 6%, Points required for next Level: 940

    Thanked 565 Times in 537 Posts

    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:


    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)

+ Reply to Thread


Tags for this Thread

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts

Advertise on Talk Stats