Normal Distribution and Standard Deviation

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What is a normal distribution?

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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.

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What is the shape of a normal distribution curve?

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The shape of a normal distribution curve is often referred to as a 'bell curve'.

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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 of the mean.

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CCSS.HSS.ID.A.4

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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 of the mean.

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CCSS.HSS.ID.A.4

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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 of the mean.

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CCSS.HSS.ID.A.4

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What is standard deviation?

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Standard deviation is a measure of the amount of variation or dispersion in a set of values.

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If the mean of a dataset is 50 and the standard deviation is 5, what is the range for 68% of the data?

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The range for 68% of the data is from 45 to 55.

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CCSS.HSS.ID.A.4

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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 from the mean.

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CCSS.HSS.ID.A.4

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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.