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) 1252 with a standard deviation of 45 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

Here, = 1252

         = 45

a) According to the empirical rule, about 68% of the data fall within one standard deviation from the mean.

= 1252 - 45 = 1207

= 1252 + 45 = 1297

Between the range 1207 and 1297, 68% of the data will be found.

b) According to the empirical rule, about 95% of the data fall within two standard deviation from the mean.

= 1252 - 2 * 45 = 1162

= 1252 + 2 * 45 = 1342

Between the range 1162 and 1342, 95% of the data will be found.

c) According to the empirical rule, about 99.7% of the data or almost all the data fall within three standard deviation from the mean.

= 1252 - 3 * 45 = 1117

= 1252 + 3 * 45 = 1387

Between the range 1117 and 1387, almost all of the data will be found.