When Serenity runs the 400 meter dash, her finishing times are normally distributed with a mean of 90 seconds and a standard deviation of 2.5 seconds. Using the empirical rule, determine the interval of times that represents the middle 95% of her finishing times in the 400 meter race.

Question

Mathematics

Diamond Lang

22 May, 01:56

When Serenity runs the 400 meter dash, her finishing times are normally distributed with a mean of 90 seconds and a standard deviation of 2.5 seconds. Using the empirical rule, determine the interval of times that represents the middle 95% of her finishing times in the 400 meter race.

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Barnett · Answer 1

[85, 95] seconds

Step-by-step explanation:

The empirical rule says 95% of the distribution is within 2 standard deviations of the mean. Two standard deviations is 2· (2.5 s) = 5 s, so 95% of her times are in the range 90 ±5 s. As an interval, that is [85, 95] seconds.