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Statistics: Polls and probability

  1. Dec 30, 2008 #1
    1. The problem statement, all variables and given/known data
    Hi all.

    At a poll in America, where 1000 people have been asked, 480 people said that they would vote yes on proposition A (it is a fictive proposition), and of course 520 people said they would vote no on proposition A.

    I have to find the probability that proposition A will pass.

    What I have done is to use the following formula:

    P = \frac{{(n + 1)!}}{{m!(n - m)!}}f^m (1 - f)^{n - m},

    which has been derived in class. Here m is 480, n is 1000. P is the probability of M persons answering "yes" out of N total (so N is the total amount of people in America voting, and M is the amount in America that votes "yes") when we have a sample of n (1000), where m (480) have answered "yes". f is equal to M/N.

    My attempt is that if more than 50% vote yes, then prop. A will pass. So I want to integrate P from N/2 to N, but it is not a continous distribution. I thought of finding P for N/2 (i.e. that 50% will answer "yes"), but that is only the probability of 50% answering yes, and does not include the rest from > 50%.

    What would be the most proper approach to this problem?

    Thanks in advance.
  2. jcsd
  3. Dec 30, 2008 #2


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    Homework Helper

    The proposition will pass if at least 50% of the voters vote for it, so your basic idea is correct.
    Try the normal approximation to find the probability you need.
  4. Dec 30, 2008 #3
    Hi statdad

    Thanks for replying. The normal approximation gives us:

    P \propto \exp \left( { - n\frac{{(f - f_0 )^2 }}{{2f_0 (1 - f_0 )}}} \right),

    where f0 is the mean, i.e. m/n. This is still a discrete distribution, so what is the next step from here?

    Thanks in advance.
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