Answer:
The variable x does have a binomial distribution. A binomial distribution has the following properties:
The experiment consists of n identical trials.
Each trial results in one of the two outcomes: success or failure.
The probability of success, denoted by p, remains constant from trial to trial.
The trials are independent.
In this case:
We have 8 identical trials (rolling a 6-sided die 8 times).
Each trial results in one of two outcomes: rolling a 4 (success) or not rolling a 4 (failure).
The probability of success (rolling a 4) remains constant at 1/6 for each roll.
Each roll of the die is independent of the others.
Therefore, x follows a binomial distribution with:
Number of trials (n) = 8
Probability of success (p) = 1/6
Explanation: