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Crossbill finches have beaks that overlap with the top beak to one side or the other of the lower beak. Most populations have 50:50 ratios of "right-handed" and "left-handed" beaks, and the handedness of the beaks is thought to be randomly determined, so we expect to see equal numbers of right-handed and left-handed finches. Consider a survey of 140 crossbill finches, which reveals 84 with right beaks and 56 with left beaks. What is the P-value of a two-sided binomial test using the normal distribution to approximate the binomial?
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