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I read Wikipedia which says that p-value is simply the area of distribution's tail. Wikipedia also says that to compute p-value of a normal distribution, you integrate over the observed range rather than infinitely (normal distribution spans infinity, AFAIK). So, I do not understand why they have upper integral bound other than $+\infty$.

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  • $\begingroup$ I was trying to say that the normal distribution has infinite range $(x, \infty)$. It is pretty infinite eventhough x is a real value. There is no need to start at $-\infty$ to arrive at infinity. $\endgroup$
    – Val
    Aug 22, 2013 at 16:45

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The calculation you refer to uses the normal distribution to approximate the binomial distribution. They integrate over the range of the binomial distribution - that's where the upper limit of the integral comes from. For a truly normal distribution one would indeed integrate to infinity.

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  • $\begingroup$ So, their switch to the normal distribution is incomplete. They switched to a new model but use parameters of the old model. AFAIK, such combination of two models may lead to chimeras. Why is it ok in this case? $\endgroup$
    – Val
    Aug 22, 2013 at 15:46
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    $\begingroup$ Terminating the limit in the integral at the range of the data (for the Normal approximation to the Binomial distribution) is unusual, but it makes no practical difference in any application where this approximation is reasonable: the difference between the two calculations is (much) smaller than the error of approximation. Usually, then, one does integrate to infinity, because such integrals are either already tabulated or are directly calculated; integrals between two finite limits are calculated as differences of two such tail areas. $\endgroup$
    – whuber
    Aug 22, 2013 at 15:57

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