For the normal distribution shown, approximately what percentage of data points lie in the shaded region?
Remember, this is the graph of the normal distribution. It has this recognisable bell curve. And it’s completely symmetrical about the mean. The total 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 multiples of the standard deviation 𝜎. This is sometimes called the 68, 95, 99.7 rule. And it tells us that approximately 68 percent of the data points lie within one standard deviation of the mean. Approximately 95 percent of them lie within two standard deviations of the mean. And it tells us that approximately 99.7 percent of the data points lie within three standard deviations of the mean.
We can see in this question that we’re interested in the percentage of data points that lie one standard deviation each side of the mean. We have seen that that’s approximately 68 percent of the data points.
So the answer to this question is 68 percent.