a. The possible values that x can assume are the whole numbers from 0 to 12. This is because x is a binomial random variable, which counts the number of "successes" (in this case, Americans who say they go to a movie theater at least once a month) in a fixed number of independent Bernoulli trials (in this case, 12 randomly selected Americans). Each trial can result in either a success or a failure, so for each of the 12 Americans, they either go to a movie theater at least once a month (success) or they do not (failure). Therefore, x can be any whole number between 0 (no one goes to a movie theater at least once a month) and 12 (everyone goes to a movie theater at least once a month)