The Normal Distribution

The Geology of Yellowstone National Park

Yellowstone National Park is home to over 10,000 geothermal features and more than 300 geysers, including Old Faithful and the Yellowstone Caldera (one of the largest calderas in the world!). The unique geology of the region and a thin continental crust are responsible for the abundance of geothermal activity.

Watch the following documentary short about Yellowstone National Park with Lisa Morgan, a research geologist at the United States Geological Survey (USGS).

✔ Discussion 1
How do you think geologists gather data, particularly over a large area or below the surface?

Normal Distribution

✔ Notes 1

A dataset is said to be normally distributed if the data distribution is shaped like a symmetrical bell curve. 
The mean of a dataset lies in the middle of the normal distribution. The percentage of the data under the curve for each section will be the same for every normally distributed dataset.
68% of the data lies within 1 standard deviation from the mean.
95% of the data lies within 2 standard deviations from the mean.
99.7% of the data lies within 3 standard deviations from the mean.

North American Continental Crust

The thickness of the earth's crust varies, depending on the location. The following image from the United States Geological Survey (USGS) illustrates this.

Draw the Normal Curve

The following table contains a random sampling of data from a study by the United States Geological Survey (USGS) of North American continental crust thickness.

✔ Calculation 1
Using your graphing calculator, run the 1-Variable Stats for this dataset to find the mean and standard deviation.
*Check out the graphing calculator tutorial on the Resources page if you have not done statistics on your calculator before.

✔ Figure 1
To draw the normal distribution curve, write the mean in the middle of the curve. Add and subtract standard deviations to determine each margin.
In each segment, record the percentage of data under the curve.

A Look at the Landscape

Each section of the normal curve always contains the same percentage of the data, so we can use this curve to estimate what percentage of the North American continental crust is a certain thickness. In areas of thicker continental crust, the landscape is probably made up of mountains. Land closer to the ocean generally has thinner continental crust.

✔ Analysis 1
What percent of the North American continental crust is greater than 44.4 kilometers thick? Using the maps, identify a portion of the United States that has crust of this thickness. What do you think the landscape looks like here?

✔ Analysis 2
What percent of the North American continental crust is between 25.8 and 44.4 kilometers thick? Using the maps, identify a portion of the United States that has crust of this thickness. What do you think the landscape looks like here?

✔ Analysis 3
What percent of the North American continental crust is less than 16.5 kilometers thick? Using the maps, identify a portion of the United States that has crust of this thickness. What do you think the landscape looks like here?

✔ Analysis 4
Refer back to the table of data. What percent of the dataset is less than 16.5 kilometers? Does this fit approximately with the normal distribution?

✔ Figure 2
A different random sampling of crust thickness yields a mean of 34.6 kilometers with a standard deviation of 9 kilometers. Draw the normal distribution curve.

​A Tour of the National Parks

Many National Parks are protected because of their unique geology. The following collaboration from USGS provides photo tours of all of the U.S. National Parks. Pick a park and take the tour. What geological aspects make the area unique? How do you think they were formed?