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) 1233 with a standard deviation of 36 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)

According to empirical rule,

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

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

= between 1233 - 1 * 36 and 1233 + 1 * 36

= between 1197 and 1269

b)

According to empirical rule,

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

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

= between 1233 - 2 * 36 and 1233 + 2 * 36

= between 1161 and 1305

c)

According to empirical rule,

Approximately 99.7% (almost all) data falls between 3 standard deviation of the mean.

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

= between 1233 - 3 * 36 and 1233 + 3 * 36

= between 1125 and 1341