7.63 Statistics Sampling Distribution?
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
Favorite Answer
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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