In a normal distribution, data is distributed in a perfect bell curve.  The mean is the middle line on the diagram.  Each vertical line on either side of the mean represents one standard deviation.  68% of the data lies within one standard deviation of the mean (this mean one standard deviation on both sides of the mean).  95% of data lies within 2 standard deviations of the mean.  99.7% of data lies within 3 standard deviations of the mean. 

Example 1: Waiting time in the ER.  The mean waiting time is 60 minutes.  The standard deviation is 10 minutes.  If the data has normal distribution, how long do 68% of people wait?

Answer to Example 1: 68% of people wait between 50 and 70 minutes.  In this question, you both add and subtract 10 (one standard deviation) from the mean to get the answer. 

*Helpful Hint: If you wanted to know how long 95% of people wait, you would add and subtract 20 minutes (2 standard deviations) from 60 (the mean) to get the answer 40-80 minutes. 

Example 2: How long do 99.7% of people wait?

Answer to Example 2: 99.7% of people wait between 30 and 90 minutes.  To get this answer, you both add and subtract 30 (3 standard deviations) from 60 (the mean).

Guide developed with assistance from S. Pruitt, student, SIUE School of Nursing, and 2014 URCA program assistant.