Results 1 to 9 of 9

Math Help - [SOLVED] Help!! The central limit theorem...

  1. #1
    Newbie
    Joined
    Dec 2009
    Posts
    5

    Exclamation [SOLVED] Help!! The central limit theorem...

    central limit theorem..
    Last edited by xoxbabigurl; December 17th 2009 at 12:25 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Oct 2009
    Posts
    218
    The Central Limit Theorem - \frac{x - \overline{x}}{s} ~ N(0,1)

    Where x is the observed value (in your case 23.5), x(bar) is the sample mean, and s is the sample standard deviation.

    You want is P(Z<23.5), but first you need to standardize it using the CLT I mentioned above to get:

    P(Z < \frac{x - \overline{x}}{s})
    and then you would just use the normal table to obtain your percentage of how many student's sample mean is less than 23.5 (that's how I interpreted what the question was asking)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Dec 2009
    Posts
    5
    so would that be 0.4286 AKA 42.86% of the 180 students which would be 77 students?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Oct 2009
    Posts
    218
    Assuming you haven't made any calculation errors (as I have not caluclated it myself) then yes.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Dec 2009
    Posts
    5
    I tackled this question differently.. I am not sure if it is right though.
    Last edited by xoxbabigurl; December 17th 2009 at 12:25 AM.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Oct 2009
    Posts
    218
    Sorry about that, made a mistake.

    I copied this from - Central limit theorem - Wikipedia, the free encyclopedia

    Let X1, X2, X3, …, Xn be a sequence of n independent and identically distributed random variables each having finite values of expectation and variance σ2 > 0. The central limit theorem states that as the sample size n increases the distribution of the sample average of these random variables approaches the normal distribution with a mean and variance σ2/n irrespective of the shape of the common distribution of the individual terms Xi.




    and Zn converges in distribution to N(0,1)

    Each Xi is the mean of Student i
    Sn is the sum of the Student's means
    X bar is the average of their averages
    and n = 180

    Now you need to find P(Z<Zn)
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Dec 2009
    Posts
    5

    Question

    So I should replace n=64 to n=180? Which gives me -2.5 which is 0.0062 which gives me 1 student =S
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Newbie
    Joined
    Dec 2009
    Posts
    5
    or should i be doing this: 0.5 - .0062 which is 0.4938
    which gives me 89 students
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Member
    Joined
    Oct 2009
    Posts
    218
    Quote Originally Posted by xoxbabigurl View Post
    So I should replace n=64 to n=180? Which gives me -2.5 which is 0.0062 which gives me 1 student =S
    Guess that's the answer, which isnt impossible (since there is a large standard error)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Central limit theorem
    Posted in the Advanced Statistics Forum
    Replies: 5
    Last Post: May 15th 2011, 08:17 AM
  2. Central limit theorem
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: January 4th 2010, 05:15 AM
  3. Replies: 13
    Last Post: February 17th 2009, 05:27 AM
  4. Central Limit Theorem
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: December 12th 2008, 12:04 PM
  5. central limit theorem
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: April 27th 2008, 08:31 AM

Search Tags


/mathhelpforum @mathhelpforum