Question 851656: Beechwood forests in East Central Europe are
being threatened by dynamic changes in land ownership and economic upheaval. The
current status of the beech tree species in this area was evaluated by Hungarian uni-
versity professors in Applied Ecology and Environmental Research (Vol. 1, 2003). The
researchers found that 25% of the beech trees in East Central Europe have been damaged
by fungi. Consider a sample of 20 beech trees from this area.
1. For any randomly selected beech tree in this area, what is the chance it has been
damaged by fungi?
2. Let X denote the number of beech trees, out of the sample, that are damaged by
fungi. What is the distribution of X? (Specify name and parameter values of
the X distribution).
3. What is the variance of X i.e. V(X)?
4. Use the PMF of X to calculate probability that in the sample there are trees
damaged by fungi i.e. P(X 6= 0)
5. Given that there are trees damaged by fungi, what is the probability only one tree
is damaged?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Researchers found that 25% of the beech trees in East Central Europe have been damagedby fungi.
Consider a sample of 20 beech trees from this area.
1. For any randomly selected beech tree in this area, what is the chance it has beend amaged by fungi?:: Ans: 0.25
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2. Let X denote the number of beech trees, out of the sample, that are damaged by fungi. What is the distribution of X? (Specify name and parameter values of
the X distribution).
Ans: Binomial because each tree is either fungal of not fungal
with probability = 0.25 for each tree.
The mean of each binomial distribution = np
In your problem n = 20 and p = 0.25
So mean = 20(0.25) = 5
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The standard deviation of each binomial distribution is sqrt(npq)
So s = sqrt(npq) = 1.9365
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3. What is the variance of X i.e. V(X) = s^2 = npq = 3.75
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4. Use the PMF of X to calculate probability that in the sample there are trees
damaged by fungi i.e. P(X = 6)
P(X = 6) = 20C6(0.25)^6(0.75)^14 = binompdf(20,0.25,6) = 0.1686
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5. Given that there are trees damaged by fungi, what is the probability only one tree is damaged?
Question?:: P(x = 1) = 20C1(0.25)*(0.75)^19 = binompdf(20,0.25,1) = 0.0211
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Cheers,
Stan H.
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