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 key parameters of a Normal Distribution?

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The key parameters are the mean (μ) which indicates the center of the distribution, and the standard deviation (σ) which measures the spread or dispersion of the distribution.

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What does the Empirical Rule state about Normal Distributions?

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The Empirical Rule states that approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

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How do you find the middle 50% of a Normal Distribution?

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The middle 50% can be found by calculating the first (25th percentile) and third quartiles (75th percentile) using the mean and standard deviation.

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What is the Z-score formula?

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The Z-score formula is Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

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What does a Z-score represent?

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A Z-score represents the number of standard deviations a data point is from the mean of the distribution.

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How do you calculate the percentage of data above a certain value in a Normal Distribution?

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You calculate the Z-score for that value and then use the Z-table to find the corresponding percentile, subtracting it from 100% to find the percentage above.

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What is the significance of the 50th percentile in a Normal Distribution?

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The 50th percentile is the median, which divides the distribution into two equal halves.

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How do you determine the cutoff for the bottom 20% in a Normal Distribution?

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To find the cutoff for the bottom 20%, you look for the 20th percentile using the Z-table and then convert it back to the original scale using the mean and standard deviation.

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What is the relationship between percentiles and Z-scores?

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Percentiles can be converted to Z-scores using the inverse of the Z-table, allowing you to find the corresponding standard deviation distance from the mean.