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) 1260 with a standard deviation of 33 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

a)

Empirical rule (68 - 95 - 99.7) rule,

Approximately, 68% data falls in 1 standard deviation of the mean.

That is between Mean - 1 SD and Mean + 1 SD

Between 1260 - 1 * 33 and 1260 + 1 * 33

Between 1227 and 1293

b)

Empirical rule (68 - 95 - 99.7) rule,

Approximately, 95% data falls in 2 standard deviation of the mean.

That is between Mean - 2 * SD and Mean + 2 * SD

Between 1260 - 2 * 33 and 1260 + 2 * 33

Between 1194 and 1326

c)

Empirical rule (68 - 95 - 99.7) rule,

Approximately, 99.7% data falls in 3 standard deviation of the mean.

That is between Mean - 3 *  SD and Mean + 3 * SD

Between 1260 - 3 * 33 and 1260 + 3 * 33

Between 1161 and 1359