Santa Fe black on white is a style of pottery that occurs inabout 61% of the pot

Question

Santa Fe black on white is a style of pottery that occurs inabout 61% of the pot shards found in the Bandelier NationalMonument area (Bandelier Archeological Excavation Project: Summer1990 Excavations at Burnt Mesa Pueblo, edited by Kohler, WasingtonState University). At on excavation site 8641 pot shards have beenfond that have not yet been cleaned and identified. What is theprobability that: a. fewer tham 5200 are Santa Fe black on whilte? 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? What is p? whatis Q? Does it appear that both np and nq are larger than 5? Why isthis an important consideration? Santa Fe black on white is a style of pottery that occurs inabout 61% of the pot shards found in the Bandelier NationalMonument area (Bandelier Archeological Excavation Project: Summer1990 Excavations at Burnt Mesa Pueblo, edited by Kohler, WasingtonState University). At on excavation site 8641 pot shards have beenfond that have not yet been cleaned and identified. What is theprobability that: a. fewer tham 5200 are Santa Fe black on whilte? 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? What is p? whatis Q? Does it appear that both np and nq are larger than 5? Why isthis an important consideration?

Explanation / Answer

Mean = 8641 x 0.61 = 5271 SD = (npq) = (8641 x 0.61 x 0.39) = 45.34 Let X be the number of Santa Fe black on white X~Binomial (5271, 45.342 ) Use this to figure out the probability (alternatively, using astatistical table) http://www.stat.tamu.edu/~west/applets/normaldemo.html a) P(X < 5200) = 0.0587 b) P(X > 5400) = 0.0022 c) P ( 5400 > X > 5200 ) = P( X > 5200) - P(X > 5400) =0.9413 - 0.0022 = 0.9391 d) n = 8641, p = 0.61, q = 0.39 Both np and nq are larger than 5. This is important as if np or nqis smaller than 5, then normal approximation to binomial problemwill not be valid. Hope this helps!

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