Empirical Rule and Normal Distributions Flashcard

Front

What is the Empirical Rule in statistics?

Back

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.

Tags

CCSS.HSS.ID.A.4

Front

In a normal distribution, what percentage of data lies below the mean?

Back

50% of the data lies below the mean in a normal distribution.

Tags

CCSS.6.SP.A.2

Front

If the mean of a normally distributed set of scores is 100 and the standard deviation is 10, what percentage of scores lies between 90 and 110?

Back

Approximately 68% of scores lie between 90 and 110.

Tags

CCSS.HSS.ID.A.4

Front

How do you calculate the percentage of data that lies above a certain value in a normal distribution?

Back

To calculate the percentage of data above a certain value, you can use the z-score formula and refer to the standard normal distribution table.

Tags

CCSS.HSS.ID.A.4

Front

What is a z-score?

Back

A z-score indicates how many standard deviations an element is from the mean. It is calculated as (X - mean) / standard deviation.

Front

What does it mean if a distribution is skewed to the right?

Back

A right-skewed distribution has a longer tail on the right side, indicating that there are a larger number of lower values and fewer higher values.

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 also the center of the distribution.

Tags

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 in a normal distribution.

Front

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

Back

Approximately 95% of the data lies within two standard deviations of the mean.

Tags

CCSS.HSS.ID.A.4

Front

If a normal distribution has a mean of 50 and a standard deviation of 5, what percentage of data lies below 40?

Back

Using the z-score, you can find that approximately 2.5% of the data lies below 40.

Tags

CCSS.HSS.ID.A.4