In a survey of adults throughout the Caribbean, 75% strongly support Caribbean integration.24 adults was selected,throughout the Caribbean, and ask if they strongly support Caribbean.
How do i know the condition for a binomial distribution are met?
http://www.math.sfu.ca/~cschwarz/Stat-301/Handouts/node67.html
This survey yields two outcomes: yes, and no. If a third response (I don't know,or maybe, or anything else, it is not a binomial distribution).
To determine if the condition for a binomial distribution is met, you need to check if the following characteristics are satisfied:
1. Fixed number of trials: Ensure that the number of trials is predetermined and remains constant. In your case, it is not explicitly mentioned whether all adults in the Caribbean were considered or if there was a specific sample size. Assuming the sample size of 24 adults is predetermined, this condition is met.
2. Independent trials: Each trial should be independent of the others. This means that the outcome of one trial should not affect the outcome of another. In your survey, if each adult is randomly selected and their responses are not influenced by others, then this condition can be considered satisfied.
3. Binary outcome: The outcome of each trial must be a "success" or "failure". In your survey, the question asked if the adults strongly support Caribbean integration, indicating a binary outcome (either support or do not support). Hence, this condition is met.
Given that all three conditions appear to be met based on the information provided, you can conclude that a binomial distribution is applicable to this scenario.