1. 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.

From the empirical rule, the probability of obtaining values within one deviation from the mean is 0.68; within two deviations is 0.95 and within 3 deviations from the mean is 0.997.

We have 99.7 % of the values within 3 deviations from the mean in our question and so the intervals are;

μ - 3σ = 80 - 3(2.5) = 73.5

μ + 3σ = 80 + 3(2.5) = 87.5

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1. 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.​

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1. 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.