Alberta forest is undergoing a pine-beetie infestation. A biologist has determin

Question

Alberta forest is undergoing a pine-beetie infestation. A biologist has determined that the number of pine-beete (1 point) A certain section of a Northern infected trees fluctuates from acre to acre, with an average of 10.2 pine-beetle infected trees per acre An acre of this forest is chosen at random and the number of pine-beetle infected pine trees is to be (a) What is the probability that between 8 and 10, inclusive, infected trees are found? ill (use four decimals in your answer) (b) What is the probability that more than 13 pine beetle infected treos will be found? Ill (use four decimals) the infected trees are to be sprayed with an insecticide at a cost of $4 for every tree infested with pine beetio(o), for equipment rental. Letting Cost represent the total cost for spraying all the pine-beetle infested trees for a randomly chosen acre of forest Find the expected cost of spraying an acre. In addition, find the standard deviation in the cost of spraying an acre E(Cost) = $ SD(Cost) = $ (use two decimals) li (use two decimals)

Explanation / Answer

Here if we say that x is the number of pine- beetle infected tree fluctuations from an random acre.

Then the distribution of x is poisson with parameter = 10.2 pine - beetle per acre

(a) Pr(8 x 10) = Pr(x 10 ; 10.2) - Pr(x < 8 ; 10.2) = 0.5580 - 0.2027 = 0.3553

(b) Pr(x > 13) = 1- Pr(x 13 ; 10.2) = 1 - 0.8495 = 0.1505

(c) here Cost = Fixed cost + variable cost = 55 + 4x

E(Cost) = E(55 + 4x) = 55+ 4 * E(x) = 55 + 4 * 10.2 = $ 95.80

SD(cost) = SD(55 + 4x) = SD(4x) = 4 * SD(x) = 4 * sqrt (10.2) = $ 12.77

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