Question

Suppose that nine Massachusetts athletes are scheduled to appear at a charity benefit. The nine are randomly chosen from eight volunteers from the Boston Celtics and four volunteers from the New England Patriots. We are interested in the number of Patriots picked.; X; X

a. There are no New England Patriots athletes chosen.

b. There is one New England Patriots athlete chosen.

c. There are two New England Patriots athletes chosen.

d. There are three New England Patriots athletes chosen.

Answer 1

The random variable X represents the number of football players picked from the nine athletes scheduled. The probability distribution of X can be calculated. The selection of athletes is done without replacement. So, the correct answer is option

Step-by-step explanation:

The random variable X represents the number of football players picked from the nine athletes scheduled to appear at the charity benefit.

b. The values that X may take on are 0, 1, 2, 3, 4, and 5.

c. The distribution of X is as follows:

P(X=0) = 1/495

P(X=1) = 9/495

P(X=2) = 36/495

P(X=3) = 84/495

P(X=4) = 126/495

P(X=5) = 99/495

The selection of athletes is done without replacement since once an athlete is selected, they are no longer available for selection.

So, the correct answer is option d.