Question

When Marques commutes to work, the amount of time it takes him to arrive is normally distributed with a mean of 37 minutes and a standard deviation of 4.5 minutes. Using the empirical rule, what percentage of his commutes will be between 23.5 and 50.5 minutes?

Answer 1

Mean ± 3σ = 37 ± 3(4.5) = 37 ± 13.5 gives 23.5 to 50.5. By the empirical rule about 99.7% of values lie within 3 standard deviations, so ≈ 99.7% of his commutes.