The total amount of vegetation held by the earth’s forests is important to both ecologists and politicians because green plants absorb carbon dioxide. An underestimate of the earth’s vegetative mass, or biomass, means that much of the carbon dioxide emitted by human activities (primarily fossilburning fuels) will not be absorbed, and a climate altering buildup of carbon dioxide will occur. Studies indicate that the biomass for tropical woodlands, thought to be about 35 kilograms per square meter (kg/m²), may in fact be too high and that tropical biomass values vary regionally—from about 5 to 55 kg/m². Suppose you measure the tropical biomass in 400 randomly selected square-meter plots.

a. Approximate σ, the standard deviation of the biomass measurements.

b. What is the probability that your sample average is within two units of the true average tropical biomass?

c. If your sample average is x̅
= 31.75, what would you conclude about the overestimation that concerns the scientists?