When Nevaeh runs the 400 meter dash, her finishing times are normally distributed with a mean of 65 seconds and a standard deviation of 1.5 seconds. Using the empirical rule, determine the interval of times that represents the middle 68% of her finishing times in the 400 meter race.
Question
When Nevaeh runs the 400 meter dash, her finishing times are normally distributed with a mean of 65 seconds and a standard deviation of 1.5 seconds. Using the empirical rule, determine the interval of times that represents the middle 68% of her finishing times in the 400 meter race.
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 Nevaeh's mean finishing time is 65 seconds and the standard deviation is 1.5 seconds, we can use the empirical rule to find the interval of times that represents the middle 68% of her finishing times.
Step 1: Calculate the lower limit of the interval. Subtract one standard deviation from the mean: 65 - 1.5 = 63.5 seconds.
Step 2: Calculate the upper limit of the interval. Add one standard deviation to the mean: 65 + 1.5 = 66.5 seconds.
Therefore, the middle 68% of Nevaeh's finishing times in the 400 meter race fall between 63.5 and 66.5 seconds.
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