1.Forests are complex, evolving ecosystems. For instance, pioneer tree species can be displaced by successional species better adapted to the changing environment. Ecologist mapped a large Canadian forest plot dominated by Douglas fir with an understory of western hemlock and western red cedar. The two-way table below records all 2050 trees in the plot by species and by life stage.

Dead Live Sapling total

Western Red 41 205 164 410

Douglas Fir 328 328 0 656

Western 472 430 82 954

hemlock

Total 841 963 246 2050

A.What Pr(Is dead)?

B.What is Pr(Is A Western Hemlock U is a Sapling)?

C.What is Pr(Is a Western Hemlock Is A Sapling)?

D.What is Pr(Is a Sapling l Western Hemlock)?

E.Are the events Sapling and Western Hemlock independent? Why or why not?

2.People with O-negative blood are universal donors. That is, any patient can receive a transfusion of O-negative blood. Only 6.6% of the American population has O-negative blood.

A.What is the probability that two randomly selected donors have O-negative blood?

B.What is the probability that five randomly selected donors do not have O-negative blood?

C.What is the probability that at least one randomly selected donor out of 5 has O-negative blood? Assume that each selection is an independent event.

3.Let x denote the lifetime (in thousands of hours) of a certain type of fan used in diesel engines. Suppose the distribution is approximately normal with a mean of = 30 and standard deviation =5.8. Answer the following questions. Give your answers as decimals rounded to 4 places for parts (a)-(d)

A.What is the probability that a randomly selected fan has a lifetime greater than 34? Symbolically Pr(X 34)

B.What is the probability that a randomly selected fan has a lifetime greater than 25 but less than 37? Symbolically Pr(25 x 37)

C.What is the probability that a randomly selected fan has a lifetime less than 28? Symbolically Pr(x28)

D.What is the probability that three randomly selected fans all have a lifetime less than 28?

5.The probability distribution of x, the number of defective tires on a randomly selected automobile checked at a certain inspection station, is given in the following table:

X01234

p(x).09?.22.27.30

A.Calculate the mean value of x, the number of defective tires on a randomly selected automobile checked at a certain inspection station.

B.What is the probability that x exceeds the mean value calculated in part b?

C.Calculate the standard deviation of x by hand.

D.What is the probability that x is within 1 standard deviation of the mean value calculated in part B?

6.Suppose that a certain metropolitan area, the probability that a household has a VCR is (=0.41). Let X denote the number of households among four households that have a VCR. Thus, x is a binomial random variable with n=4 and =0.41.

A.Calculate Pr(x = 2), show all work.

B.Calculate Pr(x = 3), show all work.

C.Determine Pr(x 2), show all work.