Question

During the NCAA basketball tournament season, affectionately called March Madness, part of one team's strategy is to foul their opponent if his free-throw shooting percentage is lower than his two-point field goal percentage. Amos's free-throw shooting percentage is lower and is only 54.7%. After being fouled he gets two free-throw shots each worth one point. Calculate the expected value of the number of points Amos makes when he shoots two free-throw shots.

Answer 1

The number of free throws, and the points he makes has a binomial distribution with the parameters n(amount of free throws) and p(probability to make the free throw).

From the text, those parameters are

`\begin{gathered} n=2 \\ p=54.7\%=0.547 \end{gathered}`

The expectation of the binomial distribution is given by

`\mu=np`

Using our values on this formula, we have

`\mu=2\cdot0.547=1.094`

The expected value of points is 1.094.