Empirical Rule - Shaded

Front

What is the Empirical Rule?

Back

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

Tags

CCSS.HSS.ID.A.4

Front

What percentage of data is within one standard deviation of the mean in a normal distribution?

Back

Approximately 68%.

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CCSS.HSS.ID.A.4

Front

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

Back

Approximately 95%.

Tags

CCSS.HSS.ID.A.4

Front

What percentage of data is within three standard deviations of the mean in a normal distribution?

Back

Approximately 99.7%.

Tags

CCSS.HSS.ID.A.4

Front

If 99.7% of the data is within three standard deviations, what percentage is outside this range?

Back

Approximately 0.3%.

Tags

CCSS.HSS.ID.A.4

Front

In a normal distribution, what does the shaded region represent?

Back

The shaded region represents the portion of data that falls within a specified number of standard deviations from the mean.

Tags

CCSS.HSS.ID.A.4

Front

If 16% of the data is in the shaded region, how many standard deviations from the mean does this represent?

Back

This represents approximately 1 standard deviation below the mean.

Tags

CCSS.HSS.ID.A.4

Front

What is the significance of the area under the normal curve?

Back

The area under the normal curve represents the total probability of all outcomes, which equals 1 (or 100%).

Tags

CCSS.7.SP.C.7A

Front

How do you calculate the percentage of data in a shaded region using the Empirical Rule?

Back

Identify the number of standard deviations from the mean that the shaded region covers and apply the corresponding percentage from the Empirical Rule.

Tags

CCSS.HSS.ID.A.4

Front

What is the percentage of data that falls between the mean and one standard deviation above the mean?

Back

Approximately 34%.

Tags

CCSS.HSS.ID.A.4