At Burnt Mesa Pueblo, archaeological studies have used the method of tree-ring d

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) 1247 with a standard deviation of 42 years. The distribution of dates was more or less mound-shaped and symmetrical 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 95% 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.

Explanation / Answer

a) According to empirical estimates, the 68% of all data lies in the range of mean plus minus 1 standard deviation. Therefore the required interval here would be:

Mean - standard deviation , Mean + standard deviation

1247 - 42, 1247 + 42

( 1205, 1289 )

b) According to empirical estimates, the 95% of all data lies in the range of mean plus minus 2 standard deviation. Therefore the required interval here would be:

Mean - 2*standard deviation , Mean + 2*standard deviation

1247 - 2*42, 1247 + 2*42

( 1163, 1331 )

c) According to empirical estimates, almost all the data lies in the range of mean plus minus 3 standard deviation. Therefore the required interval here would be:

Mean - 3*standard deviation , Mean + 3*standard deviation

1247 - 3*42, 1247 + 3*42

( 1121, 1373 )

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