For a certain section of a pine forest, the number of

Chapter 3, Problem 177E

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QUESTION:

Problem 177E

For a certain section of a pine forest, the number of diseased trees per acre, Y, has a Poisson distribution with mean λ = 10. The diseased trees are sprayed with an insecticide at a cost of $3 per tree, plus a fixed overhead cost for equipment rental of $50. Letting C denote the total spraying cost for a randomly selected acre, find the expected value and standard deviation for C. Within what interval would you expect C to lie with probability at least .75?

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QUESTION:

Problem 177E

For a certain section of a pine forest, the number of diseased trees per acre, Y, has a Poisson distribution with mean λ = 10. The diseased trees are sprayed with an insecticide at a cost of $3 per tree, plus a fixed overhead cost for equipment rental of $50. Letting C denote the total spraying cost for a randomly selected acre, find the expected value and standard deviation for C. Within what interval would you expect C to lie with probability at least .75?

ANSWER:

Solution:

Step 1 of 3:

             Given that,Y has a poisson distribution with mean

Let C denote the total spraying cost for a randomly selected acre.

  That, is C =  50 + 3Y


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