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 data.

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What percentage of data falls within one standard deviation of the mean in a Normal Distribution?

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Approximately 68% of the data falls within one standard deviation (µ ± σ) of the mean.

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What percentage of data falls within two standard deviations of the mean in a Normal Distribution?

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Approximately 95% of the data falls within two standard deviations (µ ± 2σ) of the mean.

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What percentage of data falls within three standard deviations of the mean in a Normal Distribution?

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Approximately 99.7% of the data falls within three standard deviations (µ ± 3σ) of the mean.

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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.

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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 50th percentile in a Normal Distribution?

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The 50th percentile is the median, which is also the mean in a Normal Distribution.

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How do you find the percentile rank of a score in a Normal Distribution?

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To find the percentile rank, calculate the z-score and then use the standard normal distribution table to find the corresponding percentile.