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:
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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