My Courses CRN 40938 Chapter 4 HW - Discrete Random Variable Current score: 65.5/100 points Submit assignn \( { }^{+} \)Á Category: Homework Score: 0 of 2 points Determine whether the given experiment results in a binomial distribution. If not, give the reason why not. The Traverse City Cherry Festival surveyed 100 random people in attendance, asking what their favorite fruit was, and their responses were recorded as cherries, apples, pears, or other A Not binomial; there is not a fixed number of trials B Not binomial; there are more than two outcomes for each trial C Not binomial; the trials are not independent D Not binomial; for more than one of the reasons given in the above answer choices E This experiment results in a binomial distribution Submit answer Attempts: 0/3 Find this question difficult? Do you know you can practice another version of this question?

When examining whether an experiment results in a binomial distribution, it's important to remember that binomial distributions require specific criteria: a fixed number of trials, two possible outcomes per trial (success or failure), independent trials, and a consistent probability of success. In this case, with four possible favorite fruits (cherries, apples, pears, or other), the experiment does not fit into the two-outcome requirement. Thus, you can confidently select B. Not binomial; there are more than two outcomes for each trial. So, while the cherry festival sounds delectable, the survey results yield a colorful variety, not a neat binary! To cement your understanding, consider real-life scenarios where binomial distributions apply, like flipping a coin or rolling a die. These situations typically involve only two possible outcomes—like heads and tails or rolling a 1 or not rolling a 1—making it easier to see how probability plays out in a binomial fashion. Keep practicing these principles, and soon enough, binomial distributions will be a piece of cake!