Question

When Travis goes bowling, his scores are normally distributed with a mean of 145 and a standard deviation of 12. Using the empirical rule, what percentage of the games that Travis bowls does he score between 109 and 181?

Answer 1

109 and 181 are 36 away from the mean, which is 3 standard deviations (36 = 3·12). By the empirical rule about 99.7% of values lie within ±3σ, so roughly 99.7% of his games.