Question

When Landon runs the 400 meter dash, his finishing times are normally distributed with a mean of 89 seconds and a standard deviation of 1 second. Using the empirical rule, determine the interval of times that represents the middle 95% of his finishing times in the 400 meter race.

Answer 1

Empirical rule: about 95% lie within ±2 standard deviations of the mean.

Mean = 89 s, SD = 1 s → 89 ± 2(1) = [87 s, 91 s].

So the middle 95% of his times are between 87 and 91 seconds.