Question

It is known that 10% of the trees in a Timber Supply Area (TSA) are infested with the mountain pine beetle.

e) If trees are randomly selected one at a time, what is the probability that the 4th healthy tree will be found when the 6th tree is checked?

f) A plot in this TSA contains 70 trees. What is the probability that exactly 5 trees are infested in any given plot?

g) In a given plot (70 trees), 10% of the trees are valued at $500, 700% are valued at $1,000, and 20% are valued at $2,000. What is the value of this plot? What is the standard deviation of the variable, value, for this plot?

Answer 1

e)

The probability that tree is good will be

P(good) = 1- p 0.10 = 0.90

Here we need to use negative binomial distribution with parameter r=4 and p=0.90.

The probability that the 4th healthy tree will be found when the 6th tree is checked will be

f)

Here we need to use binomial distribution with parameters n=70 and p=0.10

The probability that exactly 5 trees are infested in any given plot is

g)

Let X is a random sample shows the value of tree. Following table shows the pdf of X and calculations for mean and SD:

X	P(X=x)	xP(X=x)	x^2*P(X=x)
500	0.1	50	25000
1000	0.7	700	700000
2000	0.2	400	800000
Total		1150	1525000

So expected value of the plot is

The standard deviation is