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 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.

Answer 1

Empirical rule:

• 68% of data falls within the first standard deviation from the mean.
• 95% fall within two standard deviation from the mean.
• 99.7% fall within three standard deviation from the mean.

In this context

a) 68% of the data (tree-ring dates) will be found within  

So,  a range of years centered about the mean in which about 68% of the data (tree-ring dates) will be found
between 1204  and 1288 A.D.

b) 95 % of the data (tree-ring dates) will be found within  

So,  a range of years centered about the mean in which about 95% of the data (tree-ring dates) will be found
between 1162 and 1330 A.D.

c) All most all  the data (tree-ring dates) will be found within  

So,  a range of years centered about the mean in which almost all the data (tree-ring dates) will be found
between 1120 and 1372  A.D.