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Question 462:



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You could calculate the z-score for each runner then look up the percent of area under the normal curve, which would give you an idea of their winning percentage. We're probably ok using the z-score here since we are talking about a finite population--8 runners.

So, you'd basically add up all the runners times and calculate the grand-mean and grand standard deviation for the 8 runners by 5 races. Then you'd calculate the mean time for each runner. To find the z-score you'd then subtract the runners mean from the grand mean and divide that result by the standard deviation. This resulting z-score you would lookup in a z-table or using the z-score to percentile calculator. 

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