A biologist performs an experiment in which 2000 Asian beetles are allowed to roam in an enclosed area of 1000 square feet. The area is divided into 200 subsections of 5 square feet each.

(a) If the beetles spread evenly throughout the enclosed area, how many beetles would you expect in each subsection?

(b) What is the standard deviation of X, the number of beetles in a particular subsection?

(c) What is the probability of finding exactly eight beetles in a particular subsection?

(d) Would it be unusual to find more than sixteen beetles in a particular subsection?

Approach If the beetles spread evenly throughout the enclosed region, we can model the distribution of the beetles using Poisson probabilities.