2.4 - Empirical Rule

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 percent of data falls outside of 3 standard deviations from the mean in a normal distribution?

Back

Approximately 0.3% of the data falls outside of 3 standard deviations from the mean.

Front

If the mean life of a tire is 30,000 km and the standard deviation is 2000 km, what is the range for 68% of all tires?

Back

The range for 68% of all tires is between 28,000 km and 32,000 km.

Front

In a normal distribution, what percent of data falls between the mean and one standard deviation above the mean?

Back

Approximately 34% of the data falls between the mean and one standard deviation above the mean.

Front

What percent of people are 2 standard deviations or more above the mean in a normal distribution?

Back

Approximately 2.5% of people are 2 standard deviations or more above the mean.

Front

If the mean shelf life of a dairy product is 12 days with a standard deviation of 3 days, what percent of products last between 12 and 15 days?

Back

About 34% of the products last between 12 and 15 days.

Front

What is the GPA of the highest 2.5% of students if the mean GPA is 2.9 and the standard deviation is 0.6?

Back

The GPA of the highest 2.5% of students is 4.1 or higher.

Front

What is the significance of the standard deviation in a normal distribution?

Back

The standard deviation measures the dispersion or spread of the data points around the mean.

Front

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

Back

To calculate the range for 95% of data, take the mean and add/subtract two standard deviations.

Front

What is the area under the normal curve for one standard deviation from the mean?

Back

The area under the normal curve for one standard deviation from the mean is approximately 68%.