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) 1238 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

Solution :

Using Empirical rule,

(a)

P( - 1< X < + 1) = 68%

P(1238 - 33 < X < 1238 + 33) = 68%

P(1205 < X < 1271) = 68%

between 1205 and 1271 A.D.

(b)

P( - 2< X < + 2) = 95%

P(1238 - 2 * 33 < X < 1238 + 2 * 33) = 95%

P(1172 < X < 1304) = 95%

between 1172 and 1304 A.D.

(c)

P( - 3< X < + 3) = 99.7%

P(1238 - 3 * 33 < X < 1238 + 3 * 33) = 99.7%

P(1139 < X < 1337) = 99.7%

between  1139 and  1337 A.D.