To determine whether the given procedure results in a binomial distribution, we need to check several key characteristics of a binomial experiment:
1. Fixed Number of Trials: A binomial experiment should have a fixed number of trials. In this case, 10 different students are selected, which signifies a fixed number of selections (trials).
2. Each Trial Should Have Two Possible Outcomes: For an experiment to be binomial, each trial must result in exactly two possible outcomes. Possible outcomes should be binary, such as "success" or "failure." However, in this scenario, the possible outcomes are the GPAs of the students, which are continuous values and not binary.
3. Probability of Success Remains Constant: In a binomial distribution, the probability of success must remain the same for each trial. This characteristic doesn't directly apply here since we're looking at GPAs.
4. Independent Trials: The outcome of any given trial should not affect the outcome of another trial. In this case, students are selected without replacement, meaning once a student is selected, they cannot be selected again. This introduces dependency between trials, making them not independent.
Given these points, the most significant factor here is the nature of the outcomes. Since GPAs are continuous values and not binary outcomes, this experiment does not meet the binomial distribution criteria.
Thus, the procedure results in a non-binomial distribution for the reason that:
- There are more than two outcomes for each trial.
The correct choice is:
O Not binomial; there are more than two outcomes for each trial
