Problem

When Aaron runs the 400 meter dash, his finishing times are normally distributed with a mean of 80 seconds and a standard deviation of 2.5 seconds. Using the empirical rule, determine the interval of times that represents the middle \( 99.7 \% \) of his finishing times in the 400 meter race.

Answer

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Answer

Middle \(99.7\%\): \(\mu \pm 3\sigma = (80 - 3(2.5), 80 + 3(2.5)) = (72.5, 87.5)\)

Steps

Step 1 ：\(\mu = 80\)

Step 2 ：\(\sigma = 2.5\)

Step 3 ：Middle \(99.7\%\): \(\mu \pm 3\sigma = (80 - 3(2.5), 80 + 3(2.5)) = (72.5, 87.5)\)

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