Question

According to a Pew Research Center study, 14% of Americans have changed their views on a political or social topic in the last year because of something they saw on social media. Let the random variable be the number of people, from a random sample of 60 Americans, who have changed their political or social views in the last year because of social media.

Is the number of these people who have changed their views because of social media a binomial random variable?
A. Yes. All four conditions are met.
B. No. There is not a fixed number of trials.
C. No. The trials cannot reasonably be assumed to be independent.
D. No. The outcomes cannot be described as only "success" and failure"
E. No. The probability of success is not the same for each trial.

Answer 1

A. Yes. All four conditions are met.

Explanation:

Binomial random variable:

Can only have two outcomes(yes/no questions).

Each trial must be independent, that is, the probability of a success is always the same in a trial.

It's probabilities must be between 0 and 1.

Number of these people who have changed their views because of social media a binomial random variable.

For each people, there are only two possible outcomes. Either they did change, or they did not. For each people, the probability of changing is independent of other people, that is, the probability is the same, so yes, the conditions are met.