Normal Distribution

Front

What is a Normal Distribution?

Back

A Normal Distribution is a continuous probability distribution characterized by a symmetric bell-shaped curve, where the mean, median, and mode are all equal.

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What are the key parameters of a Normal Distribution?

Back

The key parameters are the mean (μ) which indicates the center of the distribution, and the standard deviation (σ) which measures the spread or dispersion of the distribution.

Tags

CCSS.6.SP.A.3

Front

What does the Empirical Rule state about Normal Distributions?

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The Empirical Rule states that approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

Tags

CCSS.HSS.ID.A.4

Front

How do you find the middle 50% of a Normal Distribution?

Back

The middle 50% can be found by calculating the first (25th percentile) and third quartiles (75th percentile) using the mean and standard deviation.

Tags

CCSS.6.SP.B.5C

Front

What is the Z-score formula?

Back

The Z-score formula 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 Z-score represent?

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A Z-score represents the number of standard deviations a data point is from the mean of the distribution.

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How do you calculate the percentage of data above a certain value in a Normal Distribution?

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You calculate the Z-score for that value and then use the Z-table to find the corresponding percentile, subtracting it from 100% to find the percentage above.

Tags

CCSS.HSS.ID.A.4

Front

What is the significance of the 50th percentile in a Normal Distribution?

Back

The 50th percentile is the median, which divides the distribution into two equal halves.

Tags

CCSS.6.SP.B.5C

Front

How do you determine the cutoff for the bottom 20% in a Normal Distribution?

Back

To find the cutoff for the bottom 20%, you look for the 20th percentile using the Z-table and then convert it back to the original scale using the mean and standard deviation.

Tags

CCSS.HSS.ID.A.4

Front

What is the relationship between percentiles and Z-scores?

Back

Percentiles can be converted to Z-scores using the inverse of the Z-table, allowing you to find the corresponding standard deviation distance from the mean.

Tags

CCSS.HSS.ID.A.4