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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 Empirical Rule?

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The Empirical Rule states that for a normal distribution: 68% of the data falls within 1 standard deviation, 95% within 2 standard deviations, and 99.7% within 3 standard deviations.

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CCSS.HSS.ID.A.4

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What percentage of data falls within 1 standard deviation in a normal distribution?

Back

68%

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CCSS.HSS.ID.A.4

Front

What percentage of data falls within 2 standard deviations in a normal distribution?

Back

95%

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CCSS.HSS.ID.A.4

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What percentage of data falls within 3 standard deviations in a normal distribution?

Back

99.7%

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CCSS.HSS.ID.A.4

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If the average annual precipitation in Phoenix is 29 with a standard deviation of 3, what is the normal range (68%)?

Back

26-32

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CCSS.HSS.ID.A.4

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What does it mean if data is normally distributed?

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It means that the data follows a bell-shaped curve where most of the observations cluster around the central peak and probabilities for values further away from the mean taper off equally in both directions.

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What is the significance of the mean in a normal distribution?

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The mean is the central value around which the data is distributed, and in a normal distribution, it is also the point of symmetry.

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CCSS.6.SP.B.5D

CCSS.HSS.ID.A.2

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What is the significance of the standard deviation in a normal distribution?

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The standard deviation measures the dispersion or spread of the data points around the mean; a smaller standard deviation indicates that the data points are closer to the mean.

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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.