Normal Curve

Front

What is a normal curve?

Back

A normal curve is a bell-shaped graph that represents a normal distribution, where most of the data points cluster around the mean, and the probabilities for values further away from the mean taper off equally in both directions.

Tags

CCSS.HSS.ID.A.4

Front

What is the mean in a normal distribution?

Back

The mean is the average value of a dataset, which is the center point of a normal 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 amount of variation or dispersion in a set of values. In a normal distribution, it determines the width of the curve.

Front

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

Back

Approximately 68% of the data falls within one standard deviation of the mean.

Tags

CCSS.HSS.ID.A.4

Front

What percentage of data falls between the mean and two standard deviations above the mean?

Back

Approximately 47% of the data falls between the mean and two standard deviations above the mean.

Tags

CCSS.HSS.ID.A.4

Front

What percentage of data falls between one and two standard deviations above the mean?

Back

Approximately 13.5% of the data falls between one and two standard deviations above the mean.

Tags

CCSS.HSS.ID.A.4

Front

What is the empirical rule in statistics?

Back

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

Tags

CCSS.HSS.ID.A.4

Front

How do you calculate the range for approximately 95% of data in a normal distribution?

Back

To calculate the range for approximately 95% of data, use the formula: Mean ± 2(Standard Deviation).

Tags

CCSS.HSS.ID.A.4

Front

What is the z-score in a normal distribution?

Back

The 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 data point has a z-score of 0?

Back

A z-score of 0 means the data point is exactly at the mean of the distribution.