Question

When Tallulah commutes to work, the amount of time it takes her to arrive is normally distributed with a mean of 48 minutes and a standard deviation of 4 minutes. Using the empirical rule, what percentage of her commutes will be between 36 and 60 minutes?

Answer 1

36 and 60 are 48 ± 12, which is ±3 standard deviations (12 = 3×4). By the empirical rule about 99.7% of values lie within ±3σ, so approximately 99.7% of her commutes.