Question

3.2.RA-1

According to the Empirical​ Rule, ________ will be within two standard deviations of the mean.

Answer 1

According to the Empirical Rule, approximately 95 percent of the data will be within two standard deviations of the mean for a bell-shaped distribution.

Step-by-step explanation:

According to the Empirical Rule, approximately 95 percent of the data will be within two standard deviations of the mean. This rule is a statistical fact that applies to data with a bell-shaped distribution, and helps us understand where most values fall in relation to the mean (average) of the data. When a distribution is perfectly normal, or bell-shaped, the Empirical Rule states that:

• About 68 percent of data values will lie within one standard deviation of the mean.
• About 95 percent of data values will lie within two standard deviations of the mean. This answers the question in the prompt.
• About 99.7 percent of data values will lie within three standard deviations of the mean.

Moreover, in context-specific situations, the Empirical Rule allows us to calculate the expected range for a given set of data, if the mean and standard deviations are known.