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) 1240 with a standard deviation of 26 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

Answer:

a. 1214 and 1266 A.D.

b. 1188 and 1292 A.D.

c. 1162 and 1318 A.D.

Explanation:

According to the empirical rule, in a normally distributed data set, 68% of data falls within one standard deviation above or below the mean, 95% of data falls within two standard deviations of the mean and almost all of the data is within three standard deviations of the mean.

If the mean year is 1240 and the standard deviation is 26 years:

a. 68% of data:

$1240 -26 \leq A \leq 1240+26\\1214 \leq A \leq 1266$

b. 95% of data

$1240 -(2*26) \leq B \leq 1240+(2*26)\\1188 \leq B \leq 1292$

c. Almost all data

$1240 -(3*26) \leq C \leq 1240+(3*26)\\1162 \leq C \leq 1318$