# Question Video: Estimating Areas Under a Normal Distribution Curve Mathematics

For the normal distribution shown, approximately what percent of data points lie in the shaded region?

01:40

### Video Transcript

For the normal distribution shown, approximately what percent of data points lie in the shaded region?

Remember, the total area under the curve representing a normal distribution is 100 percent. For a data distribution to be normal, we say that roughly 68 percent of the data set lies within one standard deviation of the mean. That’s this group. About 95 percent are within two standard deviations of the mean. That’s this group.

We tend to say that any data outside of this group is an outlier. So anything outside of two standard deviations of the mean, that’s the mean minus two standard deviations and the mean plus two standard deviations, is an outlier. Now roughly 99.7 percent of the data set lies within three standard deviations of the mean. That’s this shaded area.

Remember, we said that the total area under the curve is 100 hundred percent. So to calculate the percentage of the data set that lies outside three standard deviations of the mean, we’ll subtract 99.7 percent from 100. 100 minus 99.7 is 0.3. So 0.3 percent of the data set lies outside three standard deviations of the mean.

Since we’re only interested in half of this data, we’ll divide 0.3 by two. 0.3 divided by two is 0.15. So 0.15 percent of data points lie in the shaded region.