Binomial Distributions (4.2)

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What is a binomial distribution?

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A binomial distribution is a probability distribution that summarizes the likelihood that a value will take one of two independent outcomes under a given set of parameters.

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CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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What are the parameters of a binomial distribution?

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The parameters of a binomial distribution are 'n' (the number of trials) and 'p' (the probability of success on each trial).

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CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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How do you calculate the mean of a binomial distribution?

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The mean (μ) of a binomial distribution is calculated using the formula: μ = n * p.

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CCSS.HSS.ID.A.4

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What is the formula for the probability of getting exactly k successes in a binomial distribution?

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The formula is P(X = k) = (n choose k) * p^k * (1-p)^(n-k).

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CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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What does 'n choose k' mean in the context of binomial distributions?

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

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What is the probability of getting at least k successes in a binomial distribution?

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The probability of getting at least k successes is calculated as P(X ≥ k) = 1 - P(X < k).

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What is the variance of a binomial distribution?

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The variance (σ²) of a binomial distribution is calculated using the formula: σ² = n * p * (1 - p).

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How do you determine if a distribution is a probability distribution?

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A distribution is a probability distribution if all probabilities are between 0 and 1, and the sum of all probabilities equals 1.

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CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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What is the probability of rolling doubles with two dice?

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The probability of rolling doubles with two dice is 1/6.

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How do you find the probability of an event occurring more than a certain number of times in a binomial distribution?

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Use the cumulative distribution function (CDF) to find the probability of the event occurring up to that number, then subtract from 1.