Question

When Kennedy runs the 400 meter dash, her finishing times are normally distributed with a mean of 75 seconds and a standard deviation of 1.5 seconds. Using the empirical rule, what percentage of races will her finishing time be between 73.5 and 76.5 seconds

Answer 1

73.5 and 76.5 are 75 ± 1.5, i.e. μ ± 1σ. By the empirical rule about 68% of values lie within one standard deviation, so approximately 68% of her races.