Binomial Distributions (4.2)

Front

What is a Binomial Distribution?

Back

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

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What are the assumptions of a Binomial Distribution?

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1. Each trial is independent. 2. Each trial results in a success or failure. 3. The probability of success is constant across trials. 4. The number of trials is fixed.

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How do you calculate 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.

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How do you calculate the variance of a Binomial Distribution?

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

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What is the formula for standard deviation in a Binomial Distribution?

Back

Standard Deviation (σ) = √(n * p * (1 - p)).

Front

If n=50 and p=0.4, what is the mean of the distribution?

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Mean = 50 * 0.4 = 20.

Front

If n=50 and p=0.4, what is the variance of the distribution?

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Variance = 50 * 0.4 * (1 - 0.4) = 12.

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If n=50 and p=0.4, what is the standard deviation of the distribution?

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Standard Deviation = √(50 * 0.4 * 0.6) ≈ 3.5.

Front

What is the formula to find the probability of exactly k successes in n trials?

Back

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

Front

In a Binomial Distribution, what does 'n' represent?

Back

'n' represents the number of trials or experiments conducted.