(30 points, 6 points each). An insect species has been shown to kill 23% of all
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(30 points, 6 points each). An insect species has been shown to kill 23% of all pine trees that are infested with it. Suppose that in an area of forest, 20 trees are infested with the insects. Let X=# of trees killed in the forest as a result of insect damage. Answer the following: 3, a. What is the probability that exactly two trees are killed? b. What is the probability that fewer than 5 trees are killed? p (5or more)-bina mcdf (ao, . a 3,5 )-+0.6% t and P (5 or more): binam cdf Q c. What is the probability that more than 8 trees are killed? P(8 or more -1 -binomcdf Find the expected number of trees killed. expected value: mean = n p d. e. Find the standard deviation of X.Explanation / Answer
3.The random variable X=number of trees killed in the forest as a result of insect damage follows binomial distribution with parameters n=20 and p=0.23
a.Find P(X=2)
=20C2*0.23^2*0.77^18
=0.09
b.P(X<5)
=P(X=0)+…+P(X=4)
=20C2*0.23^0*0.77^20+…+20C4*0.23^4*0.77^16
=0.498
c.P(X>8)
=20C9*0.23^9*0.77^11+…+20C20*0.23^20*0.77^0
=0.024
d.The expected value is n*p=20*0.23=4.6
e.The standard deviation is rt over np(1-p)=1.88
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