Question

Saguaro cacti are large cacti indigenous to thesouthwestern United States and Mexico. Assume that thenumber of saguaro cacti in a region follows a Poisson distributionwith a mean of 280 per square kilometer. Determinethe following:(a) Mean number of cacti per 10,000 square meters.(b) Probability of no cacti in 10,000 square meters.(c) Area of a region such that the probability of at least twocacti in the region is 0.9.

Answer 1

Explanation:

Given that Saguaro cacti are large cacti indigenous to thesouthwestern United States and Mexico. Assume that thenumber of saguaro cacti in a region follows a Poisson distribution with a mean of 280 per square kilometer.

a) Mean number of cacti per 10,000 square meters=280*10000 = 2800000

b) P(no cacti in 10000) sq m = P(X=0) for Poisson with parameter 2800000

= 0

(almost uncertain event)

c) Area of a region such that the probability of at least twocacti in the region is 0.9.

`P(X\geq 2) =0.9\\`

We get this is possible if mean = 8.4 for Poisson

i.e. region should have area as

`(8.4)/(280) \\=0.03`