Questions: 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 A. Not binomial: there are too many trials. B. Not binomial: there are more than two outcomes for each trial. C. Not binomial: the trials are not independent. D. The procedure results in a binomial distribution.

Solution Steps

A binomial distribution requires the following conditions to be met:

1. A fixed number of trials \( n \).
2. Each trial has only two possible outcomes (success or failure).
3. The probability of success \( p \) is constant across trials.
4. The trials are independent.

In the given scenario, we are rolling a single die 26 times. Let's evaluate the conditions:

• Fixed Number of Trials: \( n = 26 \) (This condition is satisfied.)
• Two Possible Outcomes: Each roll of a die can result in one of six outcomes: \( 1, 2, 3, 4, 5, 6 \). Since there are more than two outcomes, this condition is not satisfied.
• Constant Probability: While the probability of rolling any specific number (e.g., rolling a \( 1 \)) is \( p = \frac{1}{6} \), this is irrelevant since the previous condition is not met.
• Independence of Trials: Each roll does not affect the others, so this condition is satisfied.

Since the second condition is not satisfied (there are more than two outcomes for each trial), the procedure does not result in a binomial distribution.

Final Answer