Michael's Arms Windmilled, Propelling Him Through the Water at a Pace

Michael's arms windmilled, propelling him through the water at a pace few could believe.He completed his 100 meter butterfly in 49.82 seconds and was pleased with his performance.At the ceremony later that afternoon, Michael and the other seven finalists were awarded participation medals, which he found distressing.He was quick to point out that the average time for the 100 meter butterfly was 53 seconds with a standard deviation of 0.9 seconds.There must be some way of demonstrating how exceptional his time was, so he turned to his friend who was studying quantitative analysis to help him prove this.How exceptional is Michael's performance?

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The Z score for his ...

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