In 2011, Detroit Tiger finished season with a .344 battign average. A .344 batting average means that he successfully reached base 34.4% of the time. Suppose that Cabrera's batting average was .344 for each of the 161 games he played in and that he batted 4 times in every game he played. Also assume that each time Cabrera bats he either gets a hit or fails to get a hit.
a. Let x be the number of hits that Cabrera had in a game in 2011. What is the distribution of X?
b. What is the expected value of X?
c. Suppose you randomly select a game that Cabrera played in from the 2011 season. What is the probability that he got exactly one hit in that game?
d. Suppose you randomly select a game that Miguel played in from the 2011 season. What is the probability that he got at least two hits in that game?