Tree-ring dates were used extensively in archaeological studies at Burnt Mesa Pu

Question

Tree-ring dates were used extensively in archaeological studies at Burnt Mesa Pueblo. At one site on the mesa, tree-ring dates (for many samples) gave a mean date of 1 = year 1252 with standard deviation 1 = 36 years. At a second, removed site, the tree-ring dates gave a mean of 2 = year 1115 with standard deviation 2 = 35 years. Assume that both sites had dates that were approximately normally distributed. In the first area, an object was found and dated as x1 = year 1205. In the second area, another object was found and dated as x2 = year 1249. (a) Convert both x1 and x2 to z values, and locate both of these values under the standard normal curve of the figure above. (Round your answers to two decimal places.) z1 = z2 = (b) Which of these two items is the more unusual as an archaeological find in its location? x1; the further a z value is from zero, the more unusual it is. x2; the further a z value is from zero, the more unusual it is. x1; the closer a z value is to zero, the more unusual it is. x2; the closer a z value is to zero, the more unusual it is.

Explanation / Answer

a)

Note that z = (x-u)/sigma.

Hence,

z1 = (1205 - 1252)/36 = -1.305555556 [ANSWER]

and

z2 = (1249 - 1115)/35 = 3.828571429 [ANSWER]

***********************

As z2 is farther from 0, it is more unusual. So,

OPTION B: x2; the further a z value is from zero, the more unusual it is. [ANSWER, B]

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