A few days ago
little bear

7.63 Statistics Sampling Distribution?

Biomass. 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 fossil-burning

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 kgs per square m (kg/m^2), may

in fact be too high and that tropical biomass values

vary regionallly from about 5 to 55 kg/m^2. Suppose

you measure the tropical biomass in 400 randomly

selected square-meter plots.

a. Approximate standard deviation of the biomass

measurement.

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 x bar = 31.75, what

would you conclude about the overestimation that

Top 1 Answers
A few days ago
Merlyn

Favorite Answer

Let X be the amount of biomass. X is uniformly distributed between 5 and 55.

In general for a uniform random variable,

the mean of the a uniform distribution between (a and b) is (a + b) / 2

the variance of the uniform distribution between (a and b) is [(a – b)^2 ]/ 12

so for this question (a) the standard deviation is Sqrt( (55-5)^2/12) = Sqrt(50^2/12) = Sqrt(208.333) = 14.433

(b) find P(33 < X < 37) integrate 1/50 dx from 33 to 37 = 2/25 = 0.08 (c) I would conclude the value of 35 is an overestimation.

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