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 most of the observations cluster around the central peak and probabilities for values further away from the mean taper off equally in both directions.

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What are the key parameters of a Normal Distribution?

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The key parameters of a Normal Distribution 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 is the Empirical Rule (68-95-99.7 Rule)?

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The Empirical Rule states that for a normal distribution: about 68% of the data falls within one standard deviation of the mean, about 95% falls within two standard deviations, and about 99.7% falls within three standard deviations.

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How do you calculate the z-score?

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The 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 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. A positive z-score indicates the value is above the mean, while a negative z-score indicates it is below the mean.

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

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The 50th percentile, also known as the median, is the value that separates the higher half from the lower half of the data set. In a normal distribution, it is equal to the mean.

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What is the area under the curve in a Normal Distribution?

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The total area under the curve of a normal distribution is equal to 1, representing the total probability of all outcomes.

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How do you find the percentage of data below a certain value in a Normal Distribution?

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To find the percentage of data below a certain value, calculate the z-score for that value and then use the standard normal distribution table (z-table) to find the corresponding area.

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

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In a normal distribution, the mean, median, and mode are all equal and located at the center of the distribution.

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What is a standard normal distribution?

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A standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1.