Statistics Standard 13 Checkpoint

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What is the normal approximation to the binomial distribution?

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The normal approximation to the binomial distribution is a method used to approximate the probabilities of a binomial distribution using a normal distribution when certain conditions are met, specifically when both np and nq are greater than or equal to 5.

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What are the conditions for using normal approximation for a binomial distribution?

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The conditions are that both np (number of successes) and nq (number of failures) must be greater than or equal to 5.

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How do you calculate the mean of a binomial distribution?

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The mean of a binomial distribution is calculated using the formula μ = np, where n is the number of trials and p is the probability of success.

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What is the standard deviation of a binomial distribution?

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The standard deviation of a binomial distribution is calculated using the formula σ = √(npq), where q = 1 - p.

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In a binomial distribution, what does 'n' represent?

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

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In a binomial distribution, what does 'p' represent?

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

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What is the probability of finding more than a certain number of successes in a binomial distribution?

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To find the probability of more than a certain number of successes, you can use the normal approximation and calculate the area under the normal curve beyond that number.

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What is the continuity correction in normal approximation?

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The continuity correction is an adjustment made when using a normal distribution to approximate a discrete distribution, typically by adding or subtracting 0.5 to the discrete value.

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What is the significance of the Central Limit Theorem in statistics?

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The Central Limit Theorem states that the distribution of the sample means will approach a normal distribution as the sample size increases, regardless of the shape of the population distribution.

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How do you determine if a normal distribution is a good approximation for a binomial distribution?

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You can determine this by checking if both np and nq are greater than or equal to 5.