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) 1246 with a standard deviation of 38 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

Ans:

Empirical rule states that for a normal distribution,68% of the data will fall within one standard deviation of the mean,95% of the data will fall within two standard deviations of the mean,Almost all (99.7%) of the data will fall within three standard deviations of the mean.

Given that

mean=1246

standard deviation=38

a)Lower limit=1246-38=1208

upper limit=1246+38=1284

b)

Lower limit=1246-2*38=1170

upper limit=1246+2*38=1322

c)

Lower limit=1246-3*38=1132

upper limit=1246+3*38=1360