Front

What is a Normal Distribution?

Back

A Normal Distribution is a continuous probability distribution characterized by a symmetric bell-shaped curve, where most of the observations cluster around the central peak and probabilities for values further away from the mean taper off equally in both directions.

Tags

CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

Front

What are the mean and standard deviation in a Normal Distribution?

Back

The mean is the average of all data points, and the standard deviation measures the dispersion or spread of the data points around the mean.

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 (±1σ) of the mean.

Tags

CCSS.HSS.ID.A.4

Front

What percentage of data falls within two standard deviations of the mean in a Normal Distribution?

Back

Approximately 95% of the data falls within two standard deviations (±2σ) of the mean.

Tags

CCSS.HSS.ID.A.4

Front

What percentage of data falls within three standard deviations of the mean in a Normal Distribution?

Back

Approximately 99.7% of the data falls within three standard deviations (±3σ) of the mean.

Tags

CCSS.HSS.ID.A.4

Front

How do you calculate the z-score?

Back

The z-score is calculated using the formula: z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

Front

What does a z-score represent?

Back

A z-score represents the number of standard deviations a data point is from the mean. A positive z-score indicates the value is above the mean, while a negative z-score indicates it is below the mean.

Front

What is the empirical rule in statistics?

Back

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

Tags

CCSS.HSS.ID.A.4

Front

How do you find the area under the curve in a Normal Distribution?

Back

The area under the curve can be found using z-scores and standard Normal distribution tables or software to determine probabilities.

Tags

CCSS.HSS.ID.A.4

Front

What is the significance of percentiles in a Normal Distribution?

Back

Percentiles indicate the relative standing of a value within a distribution, showing the percentage of data points that fall below that value.

Tags

CCSS.HSS.ID.A.4