Normal distribution and Empirical Rule

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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.

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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 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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What does the area under the standard normal curve represent?

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The area under the standard normal curve represents the probability of a random variable falling within a particular range of values.

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What is the mean in a normal distribution?

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

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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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How do you find the area to the right of a z-score?

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To find the area to the right of a z-score, you can use a standard normal distribution table or calculator to find the area to the left of the z-score and then subtract that value from 1.

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What is a z-score?

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A z-score is a statistical measurement that describes a value's relationship to the mean of a group of values, expressed in terms of standard deviations from the mean.

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What percent 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 of the mean in a normal distribution.

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What percent 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 of the mean in a normal distribution.

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What percent 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 of the mean in a normal distribution.