Normal Distribution

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What is a Normal Distribution?

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A Normal Distribution is a continuous probability distribution characterized by a symmetric bell-shaped curve, where the mean, median, and mode are all equal.

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What are the parameters of a Normal Distribution?

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The parameters of a Normal Distribution are the mean (µ) and the standard deviation (σ). The mean determines the center of the distribution, while the standard deviation measures the spread.

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What does the 68-95-99.7 rule state?

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The 68-95-99.7 rule states that in a Normal Distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

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How do you calculate a z-score?

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A z-score is calculated using the formula: z = (X - µ) / σ, where X is the value, µ is the mean, and σ is the standard deviation.

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What is the significance of percentiles in a Normal Distribution?

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Percentiles indicate the relative standing of a value within a distribution. For example, being in the 96th percentile means a value is higher than 96% of the data.

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How do you find the area under the curve for a Normal Distribution?

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The area under the curve for a Normal Distribution can be found using z-scores and standard normal distribution tables or software to determine probabilities.

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What is the empirical rule?

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The empirical rule states that for a Normal Distribution, about 68% of data falls within one standard deviation, 95% within two, and 99.7% within three standard deviations from the mean.

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What is the relationship between mean and median in a Normal Distribution?

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In a Normal Distribution, the mean and median are equal, as the distribution is symmetric around the mean.

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How do you interpret a z-score of 2?

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A z-score of 2 indicates that the value is 2 standard deviations above the mean, meaning it is higher than approximately 97.72% of the data.

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What is the purpose of standardizing a Normal Distribution?

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Standardizing a Normal Distribution allows for comparison between different distributions by converting values to z-scores.