Normal Distributions

Front

What is a normal distribution?

Back

A normal distribution is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Front

What is the mean in a normal distribution?

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The mean is the average of all data points in a distribution, representing 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 measures the amount of variation or dispersion of a set of values. In a normal distribution, it determines the width of the curve.

Front

What percentage of data lies within one standard deviation of the mean in a normal distribution?

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Approximately 68% of the data lies within one standard deviation of the mean.

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What percentage of data lies within two standard deviations of the mean in a normal distribution?

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Approximately 95% of the data lies within two standard deviations of the mean.

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What percentage of data lies within three standard deviations of the mean in a normal distribution?

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Approximately 99.7% of the data lies within three standard deviations of the mean.

Front

What is the empirical rule in statistics?

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The empirical rule states that for a normal distribution, about 68% of the data falls within one standard deviation, 95% within two, and 99.7% 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 tell you?

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A z-score indicates how many standard deviations an element is from the mean. A positive z-score indicates a value above the mean, while a negative z-score indicates a value below the mean.

Front

What is the significance of the area under the normal curve?

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The area under the normal curve represents the total probability, which equals 1 (or 100%). Each section of the curve corresponds to the probability of a value falling within that range.