At Burnt Mesa Pueblo, in one of the archaeological excavation sites, the artifact density (number of prehistoric artifacts per 10 liters of sediment) was 1.5 (Source: Bandelier Archaeological Excavation Project: Summer 1990 Excavations at Burnt Mesa Pueblo and Casa del Rito, edited by Kohler, Washington State University Department of Anthropology). Suppose you are going to dig up and examine 50 liters of sediment at this site. Let r = 0, 1, 2, 3, . . . be a random variable that represents the number of prehistoric artifacts found in your 50 liters of sediment.

(a) Explain why the Poisson distribution would be a good choice for the probability distribution of r. What is l? Write out the formula for the probability distribution of the random variable r.

(b) Compute the probabilities that in your 50 liters of sediment you will fi­nd two prehistoric artifacts, three prehistoric artifacts, and four prehistoric artifacts.

(c) Find the probability that you will fi­nd three or more prehistoric artifacts in the 50 liters of sediment.

(d) Find the probability that you will fi­nd fewer than three prehistoric artifacts in the 50 liters of sediment.