Normal Distributions: Empirical Rule 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 in a normal distribution?

Back

Approximately 68%.

Front

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

Back

Approximately 95%.

Front

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

Back

Approximately 99.7%.

Front

What is the shape of a normal distribution curve?

Back

Bell curve.

Front

If the mean of a normal distribution is 50 and the standard deviation is 5, what is the range for one standard deviation from the mean?

Back

45 to 55.

Front

What is the significance of the mean in a normal distribution?

Back

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

Front

What does it mean if data is normally distributed?

Back

It means that the data follows a symmetric bell-shaped curve, where most of the observations cluster around the central peak.

Front

How do you calculate the z-score for a value in a normal distribution?

Back

Z-score = (X - mean) / standard deviation.

Front

What is a z-score?

Back

A z-score indicates how many standard deviations an element is from the mean.