The formula to calculate the 2 Standard Deviation Rule is:
\[ \text{Range} = \mu \pm 2\sigma \]
Where:
The 2 Standard Deviation Rule, also known as the Empirical Rule, is a statistical rule which states that for a normal distribution, almost all data will fall within three standard deviations of the mean. Specifically, about 68% of data falls within one standard deviation, about 95% falls within two standard deviations, and about 99.7% falls within three standard deviations. This rule is used to determine the standard deviation of a data set and to predict where a particular data point might fall in relation to the mean.
Let's assume the following:
Step 1: Calculate the lower bound:
\[ \text{Lower Bound} = 50 - 2 \times 5 = 40 \]
Step 2: Calculate the upper bound:
\[ \text{Upper Bound} = 50 + 2 \times 5 = 60 \]
Therefore, the range within which about 95% of the data points fall is from 40 to 60.
