SOLUTION: A southern pine forest is known to be infested with pine bark beetles. It is known that 30 percent of the trees are so infested. A forester walks through the forest and selects at

Question 945987: A southern pine forest is known to be infested with pine bark beetles. It is known that 30 percent of the trees are so infested. A forester walks through the forest and selects at random 40 trees and tests to see if they have the infestation. what is the probability that of the 40 trees:
1. four trees are infested?
2. four of five trees are infested?
3. at least three trees are infested?
4. what are the mean and the variance of the distribution?
5. can the distribution by approximated by a normal distribution?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A southern pine forest is known to be infested with pine bark beetles. It is known that 30 percent of the trees are so infested. A forester walks through the forest and selects at random 40 trees and tests to see if they have the infestation. what is the probability that of the 40 trees:
Binomial Problem with n = 40 and p(infested) = 0.3
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1. four trees are infested?
P(x = 4) = 40C4*0.3^4*0.7^37 = binompdf(40,0.3,4) = 0.00196
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2. four of five trees are infested?
P(x = 4) = 5C4*0.3^4*0.7 = binompdf(5,0.3,4) = 0.02835
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3. at least three trees are infested? (out of 5 trees)
P(3<= x <=5) = 1 - binomcdf(5,0.3,2) = 1-0.8369 = 0.1631
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4. what are the mean and the variance of the distribution?
mean = np = 5*0.3 = 1.5
std = sqrt[npq] = sqrt[1.5*0.7] = 1.02
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5. can the distribution by approximated by a normal distribution?
I'll leave that to you.
Cheers,
Stan H.
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