(a) Convert both x¡ and x2 values to z values, and locate both of these values under the standard normal curve. (b) Which of these two items is the more unusual as an archaeological find in its location?

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#12 Normal Curve: Tree Rings

Tree rings dates were used extensively in archaeological studies. At one site on the mesa, tree ring dates gave a mean date of \( \mu_1 = \text{year 1272} \) with a standard deviation \( \sigma_1 = 35 \text{ years} \). At a second site, the tree ring dates gave a mean \( \mu_2 = \text{year 1122} \) with a standard deviation \( \sigma_2 = 40 \text{ years} \). 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) Convert both \( x_1 \) and \( x_2 \) values to z values, and locate both of these values under the standard normal curve.

(b) Which of these two items is the more unusual as an archaeological find in its location?
Transcribed Image Text:#12 Normal Curve: Tree Rings Tree rings dates were used extensively in archaeological studies. At one site on the mesa, tree ring dates gave a mean date of \( \mu_1 = \text{year 1272} \) with a standard deviation \( \sigma_1 = 35 \text{ years} \). At a second site, the tree ring dates gave a mean \( \mu_2 = \text{year 1122} \) with a standard deviation \( \sigma_2 = 40 \text{ years} \). 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) Convert both \( x_1 \) and \( x_2 \) values to z values, and locate both of these values under the standard normal curve. (b) Which of these two items is the more unusual as an archaeological find in its location?
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