[EX03-96] The sound of crickets chirping is a welcome summer night’s sound. In fact, those chirping crickets may be telling you the temperature.

In the book The Song of Insects, George W.

Pierce, a Harvard physics professor, presented real data relating the number of chirps per second, x, for striped ground crickets to the temperature in

°F, y. The following table gives real cricket and temperature data. It appears that the number of chirps represents an average, because it is given to the nearest tenth.

x y x y x y 20.0 88.6 15.5 75.2 15.0 79.6 16.0 71.6 14.7 69.7 17.2 82.6 19.8 93.3 17.1 82.0 16.0 80.6 18.4 84.3 15.4 69.4 17.0 83.5 17.1 80.6 16.2 83.3 14.4 76.3 Source: George W. Pierce, The Song of Insects, Harvard University Press, 1948

a. Draw a scatter diagram of the number of chirps per second, x, and the air temperature, y.

b. Describe the pattern displayed.

c. Find the equation for the line of best fit.

d. Using the equation from part

c, find the temperatures that correspond to 14 and 20 chirps, the approximate bounds for the domain of the study.

e. Does the range of temperature values bounded by the temperature values found in part d seem reasonable for this study? Explain.

f. The next time you are out where crickets chirp on a summer night and you find yourself without a thermometer, just count the chirps and you will be able to tell the temperature. If the count is 16, what temperature would you suspect it is?