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Expected value for the probability distribution.

The National Basketball Association (NBA) records a variety of statistics for each team. Two of these statistics are the percentage of field goals made by the team and the percentage of 3-point shots made by the team. For a portion of the 2004 season, the shooting records of the 29 teams in the NBA showed the probability of scoring two points by making a field goal was .44, and probability of scoring three points by making a three point shot was 0.34.

a. What is expected value of a two point shot for these teams?

b. What is expected value of a three point shot for these teams?

If the probability of making a two point shot is greater than the probability of making a three point shot, why do coaches allow some players to shoot the three point shot if they have the opportunity? Use expected value to explain your answer.

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