Question

The Chuckanut Formation is commonly found in Northern Washington. Suppose that the geologists decided to investigate a large ancient riverbed of the formation by examining each of 1000 small plots. After the investigation, they have found that only 2 plots contain fossil turtle shells from this large ancient riverbed.

a) Suppose that these plots are independent (i.e., not spatially correlated). Justify why it makes sense to assume a Poisson distribution for modeling the number of plots that contain fossil turtle shells in a large ancient riverbed of the Chuckanut Formation. Hint: You learned that a binomial distribution with a large n and a small p can be approximated 8by a Poison distribution. Do we have a large n and a small p in this situation? If so, explain in detail what they are by identifying n and p in the context of this problem.

b) Suppose that the geologists found another ancient riverbed which is 1.25 times larger than the one described above. Assuming that this ancient riverbed is similar in characteristics to the one before, what is the probability that they will find at least four plots with fossil turtle shells?

c) What is the expected number of plots with fossil turtle shells geologists will find from the ancient riverbed described in (b)?

d) The geologists will consider themselves lucky if they can find at least m plots with fossil turtle shells knowing that there is only less than 5% chance of finding more than m plots with fossil turtle shells. Find the smallest m for the ancient riverbed described in (b).

Answer 1