The table shows the probability distribution of the number of bases for a randomly selected time at bat for a San Francisco Giants player in 2010 (excluding times when the player got on base because of a walk or being hit by a pitch). In 74.29% of the at-bats the player was out, 17.04% of the time the player got a single (one base), 5.17% of the time the player got a double (two bases), 0.55% of the time the player got a triple, and 2.95% of the time the player got a home run.
a. Verify that the probabilities give a legitimate probability distribution.
b. Find the mean of this probability distribution.
c. Interpret the mean, explaining why it does not have to be a whole number, even though each possible value for the number of bases is a whole number.
San Francisco Giants Hitting
Number of Bases Probability
0................ 0.7429
1................ 0.1704
2................ 0.0517
3................ 0.0055
4................ 0.0295