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In statistics, it is taught about samples that can have some range of numbers as their values. However, in election like presidential election, there are only several candidates to choose. In that case, how can we assign assumed statistical distribution (such as normal distribution) to the poll and assign confidence interval?

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  • $\begingroup$ This sort of statistic is taught about too, just not in the courses you've had. There are lots of discrete distributions. And polling has a lot of complications. $\endgroup$
    – Peter Flom
    May 7, 2013 at 10:20

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Suppose you model each member's vote as a Bernoulli trial. Then the number of people who will vote for a candidate can be modeled with a binomial distribution. For a large population, a confidence interval based on the normal distribution can then be developed and provides a good approximation in many cases. For smaller populations, other methods can be used to construct the confidence interval.

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