From onlinestatbook's chapter on "Proportion":
Why exactly do we subtract and add these 0.5/N values? How does that make our continuous formula more "discrete"?
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1http://math.stackexchange.com/questions/416150/what-is-continuity-correction-in-statistics – Mark L. Stone Feb 27 '17 at 14:40
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Seems to be essentially a duplicate of [this](http://stats.stackexchange.com/questions/213966/why-does-the-continuity-correction-say-the-normal-approximation-to-the-binomia/). See also the extensive explanation [here](http://stats.stackexchange.com/questions/94334/continuity-correction-error-when-using-normal-distribution-to-estimate-poisson-d/94343#94343) and see some of the discussion here around cases [when it might not work](http://stats.stackexchange.com/questions/58198/using-continuity-correction-for-normal-approximation-or-not/58233#58233) – Glen_b Feb 28 '17 at 10:05
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If there are aspects of your question you think make it distinct from all of the suggestions above, please refocus the question to clearly highlight those aspects and flag to ask for it to reopen, or compose a new question – Glen_b Feb 28 '17 at 10:07