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Shortly after the introduction of a new​ coin, newspapers published articles claiming the coin is biased. The stories were based on reports that someone had spun the coin 250 times and gotten 135 heads minus that's 54​% heads.

Use the Normal model to approximate the Binomial to determine the probability of spinning a fair coin 250 times and getting at least 135 heads.

Do you think this is evidence that spinning this new coin is​ unfair? Would you be willing to use it at the beginning of a sports​ event? Explain.

 

b) Examine the probability found in part a. If the probability is low​ (less than​ 0.05), then it is not very likely that a fair coin would yield that many heads. If the probability is not​ low, then it is likely that a fair coin would yield that many heads. Determine what this indicates about the fairness of the coin. Consider with what certainty the coin could be used at the beginning of a sporting event.

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