Question: Archaeology: Pottery

Santa Fe black-on-white is a style of pottery that occurs in about 61% of the pot shards found in the Bandelier National Monument area (Bandelier Acrhaeological Excavation Project: Summer 1990 Excavations at Burnt Mesa Pueblo, edited by Kohler, Washington State University). At one excavation site 8641 pot shards have been found that have not yet been cleaned and identified. What is the probability that

a.) fewer than5200 are Santa Fe black-on-white?

b.) more than 5400 are Santa Fe black-on-white?

c.) between 5200 and 5400 are Santa Fe black-on-white?

d.) In the solution to this problem, what is n? p? q? Does it appear that both np and nq are larger than 5? Why this is an appointment consideration?