6.2 Binomial Distributions Practice

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What is a binomial distribution?

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A binomial distribution is a probability distribution that summarizes the likelihood of a value taking on two independent outcomes, typically referred to as 'success' and 'failure', over a fixed number of trials.

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What are the four conditions for a binomial experiment?

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1. The number of trials (n) is fixed. 2. Each trial has only two possible outcomes (success or failure). 3. The trials are independent. 4. The probability of success (p) is the same for each trial.

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What does 'n' represent in the binomial probability formula?

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In the binomial probability formula, 'n' represents the number of trials.

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What does 'p' represent in the binomial probability formula?

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In the binomial probability formula, 'p' represents the probability of success on a single trial.

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What does 'k' represent in the binomial probability formula?

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In the binomial probability formula, 'k' represents the number of successes in 'n' trials.

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What is the formula for calculating binomial probabilities?

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The formula for calculating binomial probabilities is P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where (n choose k) = n! / (k!(n-k)!).

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What is the mean of a binomial distribution?

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The mean (expected value) of a binomial distribution is calculated as μ = n * p.

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What is the variance of a binomial distribution?

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The variance of a binomial distribution is calculated as σ² = n * p * (1 - p).

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What is the standard deviation of a binomial distribution?

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The standard deviation of a binomial distribution is calculated as σ = √(n * p * (1 - p)).

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Can the probability of success in a binomial experiment be 0.50?

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Yes, the probability of success in a binomial experiment can be 0.50, but it is not a requirement.