Question

You roll a standard die 24 times. At the event satisfies the requirement for a binomial distribution.

a. True
b. False

Answer 1

The event of rolling a standard die 24 times satisfies the requirement for a binomial distribution.

Step-by-step explanation:

The event of rolling a standard die 24 times satisfies the requirement for a binomial distribution. The requirements for a binomial distribution are:

1. The experiment consists of a fixed number of identical trials.
2. Each trial has only two possible outcomes: success or failure.
3. The probability of success remains constant for each trial.
4. The trials are independent of each other.

Rolling a die can be considered a binomial experiment because each trial (roll) has only two possible outcomes (getting a specific number or not) and the probability of success (getting the specific number) remains constant throughout the experiment. Therefore, option a.

The statement about rolling a die 24 times fitting the conditions for a binomial distribution is true. A binomial distribution is characterized by a fixed number of independent trials, each with two possible outcomes (success or failure) and a constant probability of success on each trial. Rolling a die involves independent trials, and if you define rolling a certain number, like a five, as a success, then the probability of rolling a five is constant (1/6) each time.