Empirical Rule & Z-Score practice

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.

Front

What percentage of data falls within one standard deviation of the mean according to the Empirical Rule?

Back

Approximately 68%.

Front

What percentage of data falls within two standard deviations of the mean according to the Empirical Rule?

Back

Approximately 95%.

Front

What does the symbol 'σ' represent in statistics?

Back

Standard Deviation.

Front

If a dataset has a mean of 20 and a standard deviation of 4, what is the interval that contains approximately 99.7% of the data?

Back

The interval is 8 to 32.

Front

In a normal distribution, what is the significance of the mean?

Back

The mean is the central value around which the data is distributed.

Front

What is a Z-Score?

Back

A Z-Score indicates how many standard deviations an element is from the mean.

Front

How do you calculate a Z-Score?

Back

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

Front

What is the Z-Score for a value of 30 if the mean is 25 and the standard deviation is 5?

Back

Z = (30 - 25) / 5 = 1.

Front

What does a Z-Score of 0 indicate?

Back

A Z-Score of 0 indicates that the value is exactly at the mean.