A baseball player in the major leagues who plays regularly will have about 500 atbats (that is, about 500 times he can be the hitter in a game) during a season. Suppose a player has a 0.300 probability of getting a hit in an at-bat. His batting average at the end of the season is the number of hits divided by the number of at-bats. This batting average is a sample proportion, so it has a sampling distribution describing where it is likely to fall.
a. Describe the shape, mean, and standard deviation of the sampling distribution of the player’s batting average after a season of 500 at-bats.
b. Explain why a batting average of 0.320 or of 0.280 would not be especially unusual for this player’s yearend batting average. (That is, you should not conclude that someone with a batting average of 0.320 one year is necessarily a better hitter than a player with a batting average of 0.280.)