All-Star Baseball is a classic fantasy game that simulates the batting records of current and former all-star baseball players by dividing a circular disk into sectors (portions of the disk bounded by two radii and an arc on the disk) representing hits of various types, walks, strikeouts, fly outs, and ground outs. The ratio of the measure of the central angle of each sector on a particular all-star player's disk to $360^{\circ}$ is proportional to his hitting records. For example, a player who hit a double 6% of the times that he batted will have a "double" sector of (0.06)$\left(360^{\circ}\right)$, or $21.6^{\circ}$. When it is his turn to bat in All-Star Baseball, a player's disk is fitted on a random spinner. The spinner is spun, and the sector to which the arrow points when it stops determines the outcome of the player's time at bat. a. Would you expect a player's average hitting performance over a large number of "at-bats" in All-Star Baseball to approximate his actual batting record? Why or why not? b. Babe Ruth was one of the greatest home-run hitters in baseball history. In 1927, he hit 60 home runs, the single season record for many years. He made 691 appearances at bat that year. i. How many degrees would Ruth's home-run sector for 1927 be in All-Star Baseball? ii. When Babe Ruth (1927 disk) comes to bat in All-Star Baseball, what is the probability that he will hit a home run? c. During the 2013 season, Chris Davis hit 53 home runs, the most in major league baseball that year. On a disk based on Davis's 2013 statics, the home run sector begins at the terminal side of $76.1^{\circ}$ and ends at the terminal side of $103.9^{\circ}$. i. How many times did Davis come to bat in 2013? ii. When Chris Davis Davis (2013 disk) comes to bat in All-Star Baseball, what is the probability that he will hit a home run?