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What is the formula for the standard deviation of a binomial distribution?

Back

The standard deviation (σ) of a binomial distribution is given by the formula: σ = √(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 expected value of a binomial distribution?

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The expected value (E) of a binomial distribution is calculated using the formula: E = n * p, where n is the number of trials and p is the probability of success.

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What is the probability of getting exactly k successes in n trials in a binomial distribution?

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The probability of getting exactly k successes in n trials is given by the formula: P(X = k) = (n choose k) * p^k * (1 - p)^(n - k), where (n choose k) = n! / (k!(n-k)!).

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If the probability of success is 0.4, what is the probability of failure?

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The probability of failure is calculated as 1 - p. If p = 0.4, then the probability of failure is 1 - 0.4 = 0.6.

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What is the probability of serving pizza on the 3rd day if the probability is 0.4?

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The probability of serving pizza on the 3rd day is calculated as P(X = 1) = (1 - p)^(2) * p = (0.6)^2 * (0.4) = 0.144.

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How do you calculate the expected number of successes in a given number of trials?

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To calculate the expected number of successes, use the formula: E = n * p, where n is the number of trials and p is the probability of success.

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What is the significance of the binomial coefficient in probability calculations?

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The binomial coefficient (n choose k) represents the number of ways to choose k successes from n trials and is crucial in calculating probabilities in binomial distributions.

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What is the probability of serving pizza exactly 3 out of 5 days if the probability is 0.4?

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Using the binomial formula: P(X = 3) = (5 choose 3) * (0.4)^3 * (0.6)^2 = 0.2304.

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What does it mean if a probability is described as 'geometric'?

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A geometric probability describes the number of trials until the first success occurs, with a constant probability of success on each trial.

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What is the formula for the probability of the first success on the k-th trial in a geometric distribution?

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The probability of the first success on the k-th trial is given by: P(X = k) = (1 - p)^(k - 1) * p, where p is the probability of success.