Question

At Burnt Mesa Pueblo, archaeological studies have used the method of tree-ring dating in an effort to determine when prehistoric people lived in the pueblo. Wood from several excavations gave a mean of (year) 1246 with a standard deviation of 42 years. The distribution of dates was more or less mound-shaped and symmetric about the mean. Use the empirical rule to estimate the following:

a. a range of years centered about the mean in which about 68% of the data (tree-ring dates) will be found between _______and _____ A.D.
b. a range of years centered about the mean in Which about Of the data (tree-ring dates) will be found between______ and ________ A.D.
c. a range of years centered about the mean in Which almost all the data (tree-ring dates) Will be found between_____ and A.D.

Answer 1

(1204 ; 1288) ;

(1162 ; 1330) ;

(1120 ; 1372)

Explanation:

Given that:

Mean, m = 1246 years

Standard deviation, s = 42 years

68% is within one standard deviation the mean ;

Therefore 68% equals ;

mean ± 1(standard deviation)

(1246 - 1(42)) ; (1246 + 1(42))

1204 ; 1288

B) b. a range of years centered 95% about the mean in Which about Of the data (tree-ring dates) will be found between______ and ________ A.D.

95% is within two standard deviation of the mean ;

Therefore 95% equals ;

mean ± 2(standard deviation)

(1246 - 2(42)) ; (1246 + 2(42)

(1246 - 84) ; (1246 + 84)

(1162 ; 1330)

c. a range of years centered about the mean in Which almost all the data (tree-ring dates) Will be found between_____ and A.D.

About 99.7% which is within 3 standard deviations of the mean

99.7% is within 3 standard deviations of the mean ;

Therefore ;

mean ± 3(standard deviation)

(1246 - 3(42)) ; (1246 + 3(42))

(1120 ; 1372)