Normal Approximation to a Binomial Distribution

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What is the normal approximation to a binomial distribution?

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The normal approximation to a binomial distribution is a method used to approximate the probabilities of a binomial random variable using a normal distribution when the number of trials is large and both np and nq are greater than 5.

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What are the parameters needed to use the normal approximation for a binomial distribution?

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The parameters needed are the number of trials (n), the probability of success (p), and the probability of failure (q = 1 - p).

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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 = np.

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How do you calculate the standard deviation of a binomial distribution?

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The standard deviation (σ) of a binomial distribution is calculated using the formula σ = √(npq).

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What is the condition for using the normal approximation to a binomial distribution?

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The normal approximation can be used when both np ≥ 5 and nq ≥ 5.

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In the context of a binomial distribution, what does 'n' represent?

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

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In the context of a binomial distribution, what does 'p' represent?

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'p' represents the probability of success on a single trial.

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In the context of a binomial distribution, what does 'q' represent?

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'q' represents the probability of failure on a single trial, calculated as q = 1 - p.

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

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The probability of getting exactly k successes is given by the formula P(X = k) = (n choose k) * p^k * q^(n-k).

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What is the significance of the Central Limit Theorem in relation to the normal approximation?

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The Central Limit Theorem states that as the sample size increases, the distribution of the sample mean approaches a normal distribution, which justifies the use of normal approximation for binomial distributions with large n.