The times of the runners in a marathon are normally distributed, with a mean of 3 hours and 50 minutes and a standard deviation of 30 minute. What is the probability that a randomly selected runner has a time less than or equal to 3 hours and 20 minutes?
(Same answer using the empirical rule: recalling that approximately 68% of a normal distribution lies within one standard deviation of the mean, so that 32% lies without, and due to symmetry of the distribution you know that approximately 16% of the distribution lies to the left of one standard deviation from the mean.)
