Question 1

What is a binomial distribution?

Accepted Answer

The binomial distribution models the number of successes in a fixed number of independent trials, each with the same probability of success. It applies when there are exactly two outcomes (success/failure), the trials are independent, and the probability stays constant.

Question 2

What is the formula for binomial probability?

Accepted Answer

P(X = k) = C(n, k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successes, p is the probability of success on a single trial, and C(n, k) = n! / (k! * (n-k)!) is the binomial coefficient.

Question 3

What are the mean and standard deviation of a binomial distribution?

Accepted Answer

The mean (expected value) is n * p and the variance is n * p * (1-p). The standard deviation is the square root of the variance, sqrt(n * p * (1-p)). These describe the center and spread of the number of successes.

Question 4

When can I use the binomial distribution?

Accepted Answer

Use it when you have a fixed number of independent trials, each with exactly two outcomes and a constant success probability. Common examples include coin flips, pass/fail test results, defective-or-not items in quality control, and yes/no survey responses.

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