Chapter 7.2, Problem 12P

Normal Curve: Tree Rings Tree-ring dates were used extensively in archaeological studies at Burnt Mesa Pueblo (Bandelier Archaeological Excavation Project: Summer 1989Excavations at Burnt Mesa Pueblo, edited by Kohler, Washington State University Department of Anthropology). At one site on the mesa, tree-ring dales (for many samples) gave a mean dale of ${\mu }_{\text{1}}\text{= year}$ 1272 with standard deviation ${\sigma }_1=35$ years. At a second, removed site, the tree- ring dates gave a mean of ${\mu }_{\text{2}}\text{= year}$ 1122 with standard deviation ${\sigma }_1=40$ years. Assume that both sites had dates that were approximately normally distributed. In the first area, an object was found and dated as $x_1=\text{ year}$ 1250. In the second area, another object was found and dated as $x_2=\text{ year}$ 1234.

(a) Convertboth $x_1\text{ and }{x}_2\text{ to }z$ values, and locate both of these values under the standard normal curve of Figure 7-12.

(b) Interpretation Which of these two items is the more unusual as an archaeological find in its location?