Question

In a certain forested region, there are on average 50 trees per acre. A surveyor from the Georgia Forestry Commission counts the trees in a particular half-acre in this region. Let Y be the number of trees counted.

(a)Write the distribution that Y follows, (choosing the most appropriate distribution from the six special distributions we have studied in this course). For example, ifyou conclude that Y is binomial with parameters n=10 and p=0.5, then write Y∼Bin(10,0.5). Do not simply write Y∼Bin(n, p) without defining n and p.

(b) Find the probability that the surveyor counts between 50 and 52 trees (including 50 and 52).

Answer 1

a) Let X denotes the number of trees in a randomly selected plot of 1 acre.

Here,

X ~ Poisson(50)

The probability mass function of X is

b) The probability that the surveyor counts between 50 and 52 trees (including 50 and 52)