Binomial Distribution

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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 states and is defined by two parameters: the number of trials (n) and the probability of success (p).

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CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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What does 'n' represent in the binomial distribution?

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In the binomial distribution, 'n' represents the number of trials or experiments conducted.

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CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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What does 'p' represent in the binomial distribution?

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

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CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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

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The formula is P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where (n choose k) is the binomial coefficient.

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CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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What is the binomial coefficient?

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The binomial coefficient, denoted as (n choose k), is calculated as n! / (k!(n-k)!), where '!' denotes factorial.

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If you flip a coin 10 times, what is the probability of getting exactly 5 heads?

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Using the binomial formula, the probability is approximately 0.246.

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CCSS.HSS.MD.B.7

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What is the expected value in a binomial distribution?

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The expected value (mean) is calculated as E(X) = n * p.

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CCSS.HSS.MD.A.2

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What is the variance in a binomial distribution?

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The variance is calculated as Var(X) = n * p * (1 - p).

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What is the standard deviation in a binomial distribution?

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The standard deviation is the square root of the variance, calculated as SD = √(n * p * (1 - p)).

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What is a success in the context of binomial distribution?

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A success is defined as the outcome of interest in a binomial experiment, such as getting heads in a coin flip.