Normal Distribution

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What is a normal distribution?

Back

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 (mean), and probabilities for values further away from the mean taper off equally in both directions.

Front

What is the mean in a normal distribution?

Back

The mean is the average of all data points in a normal distribution and is located at the center of the distribution curve.

Front

What is the standard deviation in a normal distribution?

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The standard deviation is a measure of the amount of variation or dispersion in a set of values. In a normal distribution, it determines the width of the curve.

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What percentage of data falls within 1 standard deviation of the mean in a normal distribution?

Back

Approximately 68% of the data falls within 1 standard deviation of the mean.

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What percentage of data falls within 2 standard deviations of the mean in a normal distribution?

Back

Approximately 95% of the data falls within 2 standard deviations of the mean.

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What percentage of data falls within 3 standard deviations of the mean in a normal distribution?

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Approximately 99.7% of the data falls within 3 standard deviations of the mean.

Front

What is the total area under the normal distribution curve?

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The total area under the normal distribution curve is equal to 1.

Front

What does it mean if a data set is normally distributed?

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If a data set is normally distributed, it means that the data follows a pattern where most values cluster around the mean, and the probabilities of values further from the mean decrease symmetrically.

Front

What is the empirical rule in statistics?

Back

The empirical rule states that for a normal distribution: about 68% of data falls within 1 standard deviation, 95% within 2 standard deviations, and 99.7% within 3 standard deviations of the mean.

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How does the normal distribution relate to the z-score?

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The z-score indicates how many standard deviations an element is from the mean. In a normal distribution, z-scores can be used to determine the probability of a value occurring.