Results 1 to 6 of 6

Math Help - Z-Score and probability

  1. #1
    Senior Member sfspitfire23's Avatar
    Joined
    Oct 2009
    Posts
    273

    Z-Score and probability

    Fellas,

    Say I have a list of numbers (normally distributed) with a mean of -200 and a SD of 50. Now, say I would like to find the probability of getting a less than -100 and greater than +100. For the -100 I get Z=2 and for +100 I get z=6. Now I integrate against a standard normal distribution from (-infty to 2) for the -100 and from (6 to infty) for the 100 one.

    Something seems wrong with this method...Basically, I'm trying to figure out how to calculate the probability that the Dow Jones makes a 500 point swing in either direction given that its returns are normally distributed.

    Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Siron's Avatar
    Joined
    Jul 2011
    From
    Norway
    Posts
    1,250
    Thanks
    20

    Re: Z-Score and probability

    To find the probability after calculated the z-score you can also use 'the table of the normal distribution'.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    28

    Re: Z-Score and probability

    Quote Originally Posted by sfspitfire23 View Post


    Basically, I'm trying to figure out how to calculate the probability that the Dow Jones makes a 500 point swing in either direction given that its returns are normally distributed.

    Thanks!
    Then you are looking for \displaystyle P(-200-500<X<-200+500) = P(-700<X<300)

    \displaystyle = P\left(\frac{-700-(-200)}{50}<Z<\frac{300-(-200)}{50}\right)=\dots
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member sfspitfire23's Avatar
    Joined
    Oct 2009
    Posts
    273

    Re: Z-Score and probability

    Sorry pickslides, I should have been more clear. The numbers I used in the problem are not from the Dow Jones. I just used that as an example. What I understand you saying is this:

    If I want to find the probability of a 500 point swing, I should do this: P(mean-500<X<mean+500)=P(t<X<y)=P(t-mean/sigma<Z<y-mean/sigma).

    Then if I wanted the prob of just a 500 point decline it would be P(mean-500<)=P(t<X)=P(t-mean/sigma<Z) and integrate from -infty to Z.

    Right?

    Thx
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    28

    Re: Z-Score and probability

    Quote Originally Posted by sfspitfire23 View Post

    If I want to find the probability of a 500 point swing, I should do this: P(mean-500<X<mean+500)=P(t<X<y)=P(t-mean/sigma<Z<y-mean/sigma).

    Right?

    Thx
    This seems ok, but I would just use a table as suggested in post #2.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4

    Re: Z-Score and probability

    Quote Originally Posted by sfspitfire23 View Post
    Fellas,

    Say I have a list of numbers (normally distributed) with a mean of -200 and a SD of 50. Now, say I would like to find the probability of getting a less than -100 and greater than +100. For the -100 I get Z=2 and for +100 I get z=6. Now I integrate against a standard normal distribution from (-infty to 2) for the -100 and from (6 to infty) for the 100 one.

    Something seems wrong with this method...Basically, I'm trying to figure out how to calculate the probability that the Dow Jones makes a 500 point swing in either direction given that its returns are normally distributed.

    Thanks!
    What evidence do you have that they are normally distributed (or stationary)?

    CB
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Probability/Z-Score Question
    Posted in the Statistics Forum
    Replies: 1
    Last Post: October 13th 2011, 08:02 PM
  2. Probability with Z Score
    Posted in the Statistics Forum
    Replies: 1
    Last Post: March 20th 2011, 08:20 PM
  3. probability involving z-score
    Posted in the Advanced Statistics Forum
    Replies: 5
    Last Post: July 27th 2010, 10:18 PM
  4. Z-score Probability
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: December 6th 2009, 03:27 AM
  5. Probability to X-score
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: June 27th 2008, 11:08 PM

Search Tags


/mathhelpforum @mathhelpforum