Exercise 14 Page 808

Let's look at the given bar graph representing the probability distribution.

We can see that the number of shots made represents $X$ in this distribution. A probability distribution needs to satisfy two conditions to be valid.

• The probability of each value of $X$ is greater than or equal to $0$ and less than or equal to $1.$
• The sum of the probabilities of all values of $X$ is $1.$

Looking at the graph, we can see that the probability of each value of $X$ is greater than $0$ and less than $1.$ Looking closely at the height of the bars, we can see that the values are about $0.55,$ $0.25,$ $0.14,$ and $0.04.$ Let's draw a line in between the horizontal lines to see this clearly.

We can see that the two probabilities to the right are slightly less than halfway. Let's add up our estimations. The probabilities do not add up to $1.$ This makes the distribution not valid.