Answered: Tree-ring dates were used extensively…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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 1261 with standard deviation ?₁ = 38 years. At a second, removed site, the tree-ring dates gave a mean of ?₂ = year 1100 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 1207. In the second area, another object was found and dated as x₂ = year 1244.

(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.)

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

A. x1; the further a z value is from zero, the more unusual it is.

B. x2; the further a z value is from zero, the more unusual it is.

C. x1; the closer a z value is to zero, the more unusual it is.

D. x2; the closer a z value is to zero, the more unusual it is.

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 u, = year 1261 with standard deviation o, = 38
years. At a second, removed site, the tree-ring dates gave a mean of u, = year 1100 with standard deviation o, = 35 years. Assume that both sites had dates that were approximately normally distributed. In the first area,
an object was found and dated as x, = year 1207. In the second area, another object was found and dated as x, = year 1244.
The Standard Normal Distribution
(u = 0, o = 1)
-2
68% of area
95% of area
99,7% of area
(a) Convert both x, and x, 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.)
z, =
Z2 =
(b) Which of these two items is the more unusual as an archaeological find in its location?
O x,; the further a z value is from zero, the more unusual it is.
O x,; the further a z value is from zero, the more unusual it is.
O x,; the closer a z value is to zero, the more unusual it is.
O x3; the closer a z value is to zero, the more unusual it is.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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