Binomial Distribution

Front

What are the assumptions of the Binomial distribution?

Back

1. There are a fixed number of trials. 2. Each trial has two possible outcomes (success or failure). 3. The probability of success is constant for each trial. 4. The trials are independent.

Front

What is the formula for calculating the probability of exactly k successes in n trials in a Binomial distribution?

Back

P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where p is the probability of success.

Front

What does 'n choose k' represent in the Binomial formula?

Back

'n choose k' (denoted as C(n, k) or nCk) represents the number of ways to choose k successes from n trials.

Front

How do you calculate the probability of at least k successes in a Binomial distribution?

Back

P(X ≥ k) = 1 - P(X < k) = 1 - Σ P(X = i) for i = 0 to k-1.

Front

What is the mean (expected value) of a Binomial distribution?

Back

The mean is given by μ = n * p, where n is the number of trials and p is the probability of success.

Front

What is the variance of a Binomial distribution?

Back

The variance is given by σ² = n * p * (1 - p), where n is the number of trials and p is the probability of success.

Front

What is the standard deviation of a Binomial distribution?

Back

The standard deviation is given by σ = √(n * p * (1 - p)).

Front

What does P(X > k) represent in a Binomial distribution?

Back

P(X > k) represents the probability of having more than k successes in n trials.

Front

What does P(X < k) represent in a Binomial distribution?

Back

P(X < k) represents the probability of having fewer than k successes in n trials.

Front

What does P(X ≤ k) represent in a Binomial distribution?

Back

P(X ≤ k) represents the probability of having at most k successes in n trials.