When Easton runs the 400 meter dash, his finishing times are normally distributed with a mean of 80 seconds and a standard deviation of 3 seconds. Using the empirical rule, determine the interval of times that represents the middle 68% of his finishing times in the 400 meter race.
Question
When Easton runs the 400 meter dash, his finishing times are normally distributed with a mean of 80 seconds and a standard deviation of 3 seconds. Using the empirical rule, determine the interval of times that represents the middle 68% of his finishing times in the 400 meter race.
Solution
The empirical rule, also known as the 68-95-99.7 rule, states that for a normal distribution, 68% of the data falls within one standard deviation of the mean.
Given that Easton's mean finishing time is 80 seconds and the standard deviation is 3 seconds, we can use the empirical rule to find the interval of times that represents the middle 68% of his finishing times.
Step 1: Calculate the lower limit of the interval. This is done by subtracting one standard deviation from the mean.
80 - 3 = 77 seconds
Step 2: Calculate the upper limit of the interval. This is done by adding one standard deviation to the mean.
80 + 3 = 83 seconds
Therefore, the middle 68% of Easton's finishing times in the 400 meter race fall between 77 and 83 seconds.
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