The basketball player from Example 2 is asked to shoot three free throws 100 times. Compute the mean number of free throws made.

Approach The player shoots three free throws and the number made is recorded. We repeat this experiment 99 more times and then compute the mean number of free throws made.

Data from Example 2

Suppose we ask a basketball player to shoot three free throws. Let the random variable X represent the number of shots made, so x = 0, 1, 2, or 3. Table 1 shows a probability distribution for the random variable X.

We denote probabilities using the notation P(x), where x is a specific value of the random variable. We read P(x) as “the probability that the random variable X equals x.” For example, P(3) = 0.51 is read “the probability that the random variable X equals 3 is 0.51.”

Table 1 x P(x) 0 0.01 1 0.10 2 0.38 3 0.51