Use the following for questions 3 and 4: You examine each tree in a 25-foot by 2

Question

Use the following for questions 3 and 4: You examine each tree in a 25-foot by 25-foot section of forest and record whether or not that tree is infected by the pine shoot moth. Based on historical data, the average number of trees that would be expected to be infected in a section of this size is 3.

What is the probability you would find at least 2 infected trees in a section of this size?

Select one:

a. 0.7760

b. 0.2240

c. 0.5768

d. 0.8009

Due to budget cuts, you will only be able to examine the trees in an area half as large as originally intended. About how many infected trees can you expected to see in an area that is half as large?

Select one:

a. 3

b. 2.4

c. 1.5

d. 0.33

Explanation / Answer

Ans:

1)Poisson distribution with average rate=3

P(atleast 2)=P(x>=2)=1-P(x<=1)=1-P(x=0)-P(x=1)

=1-e-3*(30/0!)-e-3(31/1!)

=1-e-3*(1+3)=1-0.1991=0.8009

Option d is correct(0.8009)

2)When area is halved,average rate will also be halved.

So,we are expected to see on average 1.5 infected trees in the half area.

Option c is correct(1.5)

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