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) 1256 with a standard deviation of 41 years. The distribution of dates was more or less mound-shaped and symmetrical 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

Result:

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) 1256 with a standard deviation of 41 years. The distribution of dates was more or less mound-shaped and symmetrical 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 1215  and 1297 A.D.

1256-41=1215

1256+41=1297

(b) a range of years centered about the mean in which about 95% of the data (tree-ring dates) will be found between 1174 and   1338 A.D.

1256-2*41=1174

1256+2*41=1338

(c) a range of years centered about the mean in which almost all the data (tree-ring dates) will be found between 1133 and 1379 A.D.

1256-3*41=1133

1256+3*41=1379

Note:

The empirical rule states that for a normal distribution, nearly all of the data will fall within three standard deviations of the mean. The empirical rule states that

68% of data falls within the first standard deviation from the mean.

95% fall within two standard deviations.

99.7% fall within three standard deviations.