What is a binomial distribution?

What is a binomial distribution?

• A. A binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes.
• B. It describes a continuous variable distribution
• C. It describes the distribution of sample means
• D. It describes the distribution of variances across samples

Answer: (A)

Binomial distribution counts how many times a binary outcome occurs in a fixed number of independent trials, with the same chance of success on every trial. It is discrete, allowing values from 0 to n, where n is the number of trials and p is the probability of success on each trial. The probability of exactly k successes is P(X = k) = C(n, k) p^k (1 − p)^(n − k). This fits situations like flipping a coin n times and counting how many heads you get, or counting how many items pass quality control in a batch. The other descriptions refer to different kinds of distributions: a continuous variable distribution, the sampling distribution of the mean, or the sampling distribution of variances, none of which capture the count of successes in fixed independent trials.

Binomial distribution counts how many times a binary outcome occurs in a fixed number of independent trials, with the same chance of success on every trial. It is discrete, allowing values from 0 to n, where n is the number of trials and p is the probability of success on each trial. The probability of exactly k successes is P(X = k) = C(n, k) p^k (1 − p)^(n − k). This fits situations like flipping a coin n times and counting how many heads you get, or counting how many items pass quality control in a batch. The other descriptions refer to different kinds of distributions: a continuous variable distribution, the sampling distribution of the mean, or the sampling distribution of variances, none of which capture the count of successes in fixed independent trials.