For a normally distributed data set, approximately what percentage of data points will lie within one standard deviation of the mean?
The graph of the normal distribution is a bell-shaped curve. And it’s completely symmetrical about the mean. The area under the curve is one or 100 percent. And we can model our data by considering its distance from the mean in terms of the standard deviation 𝜎. And this is sometimes called the 68-95-99.7 rule.
And it tells us that approximately 68 percent of data points will lie within one standard deviation of the mean. It tells us that approximately 95 percent of data points lie within two standard deviations of the mean. And finally, it tells us that 99.7 percent of our data points will lie within three standard deviations of the mean.
In this question, we’re looking to find the percentage of data points that will lie within one standard deviation of the mean. We said that that was 68. So our answer to this question is 68 percent.