The Normal Distribution Practice

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What is the normal distribution?

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The normal distribution is a continuous probability distribution characterized by a symmetric bell-shaped curve, defined by its mean (average) and standard deviation (spread). It describes how the values of a variable are distributed.

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What is the mean in a normal distribution?

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The mean is the average value of a set of data points in a normal distribution, and it is the center of the distribution curve.

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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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What is the Empirical Rule?

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The Empirical Rule states that for a normal distribution: approximately 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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How do you calculate the percentage of data that falls outside a specified range in a normal distribution?

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To calculate the percentage of data that falls outside a specified range, you can use the cumulative distribution function (CDF) to find the probabilities of the lower and upper bounds, then subtract these from 1.

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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 in a normal distribution.

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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 in a normal distribution.

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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 in a normal distribution.

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How do you find the z-score for a value in a normal distribution?

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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 is a z-score?

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A z-score indicates how many standard deviations a data point is from the mean of the distribution. It can be positive or negative.