Question

At Burnt Mesa Pueblo, in one of the archaeological excavation sites, the artifact density (number of prehistoric artifacts per 10 liters of sediment) was 1.2. Suppose you are going to dig up and examine 49 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 49 liters of sediment.

(a) Explain why the Poisson distribution would be a good choice for the probability distribution of r.

Finding prehistoric artifacts is a rare occurrence. It is reasonable to assume the events are independent.Finding prehistoric artifacts is a common occurrence. It is reasonable to assume the events are independent.    Finding prehistoric artifacts is a common occurrence. It is reasonable to assume the events are dependent.Finding prehistoric artifacts is a rare occurrence. It is reasonable to assume the events are dependent.

What is λ?


Write out the formula for the probability distribution of the random variable r. (Use e, λ, and r in your answer.)
P(r) =

(b) Compute the probabilities that in your 49 liters of sediment you will find two prehistoric artifacts, three prehistoric artifacts, and four prehistoric artifacts. (Round your answers to four decimal places.)

P(2) =
P(3) =
P(4) =

(c) Find the probability that you will find three or more prehistoric artifacts in the 49 liters of sediment. (Round your answer to four decimal places.)


(d) Find the probability that you will find fewer than three prehistoric artifacts in the 49 liters of sediment. (Round your answer to four decimal places.)

Answer 1

a) The number of prehistoric artifacts in 49 liters of sediment at this site is not too large and not too small ans is also an integer. So the Poisson distribution would be a good choice for the probability distribution of .

The Poisson parameter (mean) for 49 liters of sediment at this site is .

The probability distribution of the random variable is

b)The probabilities are calculated below.

c) The probability,

d)The probability,