Great hitters then and now. Three landmarks of baseball achievement are Ty Cobb's batting average of .420 in 1911, Ted Williams's .406 in 1941, and George Brett's .390 in 1980. These batting averages cannot be compared directly because the distribution of major league batting averages has changed over the years. The distributions are quite symmetric and (except for outliers such as Cobb, Williams, and Brett) reasonably Normal. While the mean batting average has been held roughly constant by rule changes and the balance between hitting and pitching, the standard deviation has dropped over time. Here are the facts:

Decade: Mean: Std. Dev.

1910s .266 .0371

1940s .267 .0326

1970s .261 .0317

A. Compute the standard scores for the batting averages of Cobb, Williams, and Brett to compare how far each stood above his peers. B. According to ESPN, the batting average leaders in 2018 were Mookie Betts of the Boston Red Sox for the American League (AL) and Christian Yelich of the Milwaukee Brewers for the National League (NL). AL batting averages had a mean of .262 with standard deviation .0315, while NL batting averages had a mean of .269 with standard deviation .0233. Use standard scores to compare the batting averages for Betts and Yelich. Which player performed better relative to his peers?