Normal Distribution

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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 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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CCSS.HSS.ID.A.2

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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.

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What does the empirical rule state?

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

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68%.

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

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95%.

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

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99.7%.

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If the mean is 12 days and the standard deviation is 3 days, what percent of products last between 12 and 15 days?

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34%.

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In a normal distribution, what does it mean if a data point is one standard deviation above the mean?

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It means that the data point is higher than the average value and falls within the upper 34% of the distribution.

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How do you calculate the z-score for a data point?

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The z-score is calculated using the formula: z = (X - μ) / σ, where X is the data point, μ is the mean, and σ is the standard deviation.