Race times at the local monthly 5k run are normally distributed, with a mean time of 32 minutes and a standard deviation of 4 minutes. Using the empirical rule, approximately what percent of racers cross the finish line between 28 and 36 minutes? 32% 68% 95% 99.7%

Question

Denzel Vaughn

Mathematics

1 November, 03:08

Race times at the local monthly 5k run are normally distributed, with a mean time of 32 minutes and a standard deviation of 4 minutes. Using the empirical rule, approximately what percent of racers cross the finish line between 28 and 36 minutes? 32% 68% 95% 99.7%

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Robert Maddox · Answer 1

68%

Step-by-step explanation:

The mean is 32 minutes, and the standard deviation is 4 minutes.

28 is 1 standard deviation below the mean, and 36 is 1 standard deviation above the mean.

According to the empirical rule, 68% of a normal distribution is between - 1 and 1 standard deviations. 95% is between - 2 and 2 standard deviations. 99.5% is between - 3 and 3 standard deviations.

So the answer is 68%.