Binomial Probability Distribution

Front

What is the formula for the mean of a binomial distribution?

Back

Mean (μ) = n * p, where n is the number of trials and p is the probability of success.

Front

If p = 82%, what is q?

Back

q = 1 - p = 0.18.

Front

What does the binomial probability formula calculate?

Back

It calculates the probability of getting exactly k successes in n independent Bernoulli trials.

Front

What is the binomial probability formula?

Back

P(X = k) = (n choose k) * p^k * q^(n-k), where q = 1 - p.

Front

In a binomial distribution, what does 'n' represent?

Back

'n' represents the number of trials or experiments.

Front

In a binomial distribution, what does 'p' represent?

Back

'p' represents the probability of success on a single trial.

Front

What is the probability of getting exactly 5 successes in 6 trials if p = 0.7?

Back

P(X = 5) = (6 choose 5) * (0.7)^5 * (0.3)^1 = 0.3025.

Front

What is the variance of a binomial distribution?

Back

Variance (σ²) = n * p * q.

Front

If a restaurant has a 70% chance of having yellow flowers on tables, what is the probability of 5 out of 6 tables having yellow flowers?

Back

P(X = 5) = (6 choose 5) * (0.7)^5 * (0.3)^1 = 0.3025.

Front

What is the standard deviation of a binomial distribution?

Back

Standard deviation (σ) = √(n * p * q).