Normal Distributions and Z-scores

Front

What is a normal distribution?

Back

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.

Front

What does a Z-score represent?

Back

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

Front

How do you calculate a Z-score?

Back

Z-score = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

Front

What is the mean (μ) in a normal distribution?

Back

The mean (μ) is the average of all data points in a distribution.

Tags

CCSS.HSS.ID.A.2

CCSS.6.SP.B.5D

Front

What is the standard deviation (σ) in a normal distribution?

Back

The standard deviation (σ) measures the amount of variation or dispersion of a set of values.

Front

If a Z-score is positive, what does it indicate?

Back

A positive Z-score indicates that the data point is above the mean.

Front

If a Z-score is negative, what does it indicate?

Back

A negative Z-score indicates that the data point is below the mean.

Front

What is the significance of a Z-score of 0?

Back

A Z-score of 0 indicates that the data point is exactly at the mean.

Front

What is the empirical rule in relation to normal distributions?

Back

The empirical rule states that approximately 68% of 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

Calculate the Z-score for a score of 85, with a mean of 75 and a standard deviation of 10.

Back

Z-score = (85 - 75) / 10 = 1.0.