Chapter 3, Problem 17CR

Focus Problem: Water Solve the focus problem at the beginning of this chapter.

The Yellowstone River starts in massive and beautiful Yellowstone Lake. Then it flows through prime trout fishing areas to the famous Yellowstone Falls. After it leaves the park, the river is an important source of water for wildlife, ranchers, farmers, and cities downstream. How much water does leave the park each year? The annual flow of the Yellowstone River (units $10°$ cubic meters) is shown here for 19 recent years (Reference: U.S. Department of Interior. U.S. Geological Survey: Integrated Geoscience Studies in the Greater Yellowstone Area).

25.9	32.4	33.1	19.1	17.5	24.9
27.1	29.1	25.6	31.8
21.0	45.1	30.8	34.3	25.9	18.6
23.7	24.1	23.9

(a) Is there a "guaranteed" amount of water farmers, ranchers, and cities will get from the Yellowstone River each year?

(b) What is the “expected” annual How from the Yellowstone snowmelt? Find the mean, the median, and the mode.

(c) Find the range and standard deviation of annual flow.

(d) Find a 75% Chebyshev interval around the mean.

(e) Give a five-number summary of annual water How from the Yellowstone River and make a box-and-whisker plot. Interpret the five-number summary and the box-and-whisker plot. Where does the middle portion of the data lie? What is the interquartile range? Can you find data withers?

(f) The Madison River is a smaller but very important source of water flowing out of Yellowstone Park from a different drainage. Ten recent years of annual water flow data are shown below (units $10°$ cubic meters).

3.83

3.81

4.01

4.84

5.81

5.50

4.31

5.81

4.31

4.67

Although smaller, is the Madison more reliable? Use the coefficient of variation to make an estimate.

(g) Interpretation Based on the data, would it be safe to allocate at least 27 units of Yellowstone River water each year for agricultural and domestic use? Why or why not?