Question

When Xochitl runs the 400 meter dash, her finishing times are normally

distributed with a mean of 84 seconds and a standard deviation of 2.5
seconds. Using the empirical rule, determine the interval of times that
represents the middle 68% of her finishing times in the 400 meter race.

Answer 1

Answer: The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

In this case, the mean of Xochitl's finishing times is 84 seconds and the standard deviation is 2.5 seconds, so the interval that represents the middle 68% of her finishing times is:

[84 - 2.5, 84 + 2.5] = [81.5, 86.5]

So, we can conclude that the middle 68% of Xochitl's finishing times in the 400 meter race fall between 81.5 and 86.5 seconds.

Explanation: