Refer to Exercise 48. Use the 68–95–99.7 rule to answer the following questions.

a. About what percent of Major League Baseball players with 100 plate appearances had batting averages of 0.363 or higher? Show your method clearly.

b. A player with a batting average of 0.227 is at about what percentile in this distribution? Justify your answer.

Exercise 48.

In baseball, a player’s batting average is the proportion of times the player gets a hit out of his total number of times at bat. The distribution of batting averages in a recent season for Major League Baseball players with at least 100 plate appearances can be modeled by a Normal distribution with mean μ = 0.261 and standard deviation σ=0.034 . Sketch the Normal density curve. Label the mean and the points that are 1, 2, and 3 standard deviations from the mean.