Empirical Rule and Normal Distribution

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, about 95% falls within two standard deviations, and about 99.7% falls within three standard deviations.

Front

What is a normal distribution?

Back

A normal distribution is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Front

What shape does a normal distribution curve have?

Back

A normal distribution curve has a bell shape.

Front

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

Back

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

Front

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

Back

95% of the data falls within two standard deviations of the mean.

Front

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

Back

99.7% of the data falls within three standard deviations of the mean.

Front

If the mean shelf life of a dairy product is 12 days and the standard deviation is 3 days, what is the shelf life range for 68% of the products?

Back

The shelf life range for 68% of the products is between 9 days (12-3) and 15 days (12+3).

Front

In a normal distribution, what does it mean if a data point is one standard deviation above the mean?

Back

It means that the data point is higher than approximately 84% of the data points in the distribution.

Front

How do you calculate the percentage of data between two points in a normal distribution?

Back

Use the Empirical Rule or Z-scores to find the area under the curve between the two points.

Front

What is the Z-score formula?

Back

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