Determine whether the given procedure results in a binomial distribution. If not, state the reason why. Rolling a single die 26 times, keeping track of the numbers that are rolled.
Not binomial: there are too many trials.
Not binomial: the trials are not independent.
The procedure results in a binomial distribution.
Not binomial: there are more than two outcomes for each trial.

The procedure described — rolling a single die 26 times and keeping track of the numbers that are rolled — **does not result in a binomial distribution** because there are more than two possible outcomes for each trial.

### Explanation:
A binomial distribution requires:
1. A fixed number of trials.
2. Only two possible outcomes for each trial (success or failure).
3. Each trial must be independent.
4. The probability of success is the same for each trial.

In this case:
- Rolling a die has **6 possible outcomes** (numbers 1 through 6), not just two.
- Thus, it violates the requirement of having only two outcomes per trial, so the distribution cannot be binomial.

### Conclusion:
The correct answer is:
**Not binomial: there are more than two outcomes for each trial.**

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Would you like more details or have any other questions? Here are 5 related questions that could expand on this topic:

1. What are some examples of binomial distributions in real life?
2. How does the probability of success impact the shape of a binomial distribution?
3. Can rolling a die be transformed into a binomial experiment under certain conditions?
4. What is the difference between binomial and multinomial distributions?
5. How can we calculate the expected value in a binomial distribution?

**Tip:** To classify a problem as binomial, always check if the outcomes can be simplified into two categories, like "success" and "failure."

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. Rolling a single die 26 times, keeping track of the numbers that are rolled.

Explore whether rolling a single die 26 times results in a binomial distribution. Understand why the number of possible outcomes (6 for a die) violates the two-outcome requirement for a binomial experiment. Learn the conditions necessary for a binomial distribution and apply them to real-world examples. Suitable for students in Grades 10-12.

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