z-Scores and Normal Distributions

Front

What is a z-score?

Back

A z-score indicates how many standard deviations an element is from the mean of a data set.

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How do you calculate a z-score?

Back

The formula for calculating a z-score is: 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 positive z-score indicate?

Back

A positive z-score indicates that the value is above the mean.

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What does a negative z-score indicate?

Back

A negative z-score indicates that the value is below the mean.

Front

What is the mean in a normal distribution?

Back

The mean is the average of all data points in a normal distribution and is located at the center of the distribution.

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CCSS.6.SP.B.5D

CCSS.HSS.ID.A.2

Front

What is the standard deviation in a normal distribution?

Back

The standard deviation measures the dispersion or spread of the data points around the mean.

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What is the empirical rule (68-95-99.7 rule)?

Back

The empirical rule states that in a normal distribution: 68% of 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

Front

What is the area under the normal curve?

Back

The total area under the normal distribution curve is equal to 1, representing the total probability.

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What is InvNorm?

Back

InvNorm is a function used to find the z-score that corresponds to a given cumulative probability in a normal distribution.

Tags

CCSS.HSS.ID.A.4

Front

How do you find the probability of a z-score?

Back

You can find the probability of a z-score using a z-table or a calculator that provides cumulative probabilities.

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CCSS.HSS.ID.A.4