2 61009 At Burnt Mesa Pueblo, a dating in an effort to people lived in the puebl

Question

2 61009 At Burnt Mesa Pueblo, a dating in an effort to people lived in the pueblo. Wood from several excavations gave a mean of (year) 1239 with a standard deviation of 34 years. The distribution of dates was more or less mound-shaped and symmetric about the mean. Use the empirical rule to estimate the folowing. (a) a range of years centered about the mean in which about 68% of the data (tree-ring dates) w be found X and 1293 (b) range or years centered about the mean in which about 95% of the data (tree-ring dates) will be found X and 132 (c) a range of years centered about the mean in which almost all the data (tree-ring dates) will be found X A.D. x and 1361 3 6

Explanation / Answer

a) According to the emprical rule 68% of the data will be remain bettween one standard deviation from the mean.

So the values are :

1239 - 34, 1239 + 4

= 1205, 1273

So the 68% data will be found between 1205 and 1273

b) According to the emprical rule 95% of the data will be remain bettween two standard deviation from the mean.

so the values are:

1239 - 2 * 34, 1239 + 2 * 34

= 1239 - 68, 1239 + 86

= 1171, 1325

So the 95% data will be found between 1171 and 1325.

c) According to the emprical rule almost all the data(99.7% of the data) will be remain bettween three standard deviation from the mean.

so the values are

1239 - 3 * 34, 1239 + 3* 34

= 1239 - 102, 1239 + 103

= 1137, 1341

So almost all the data will be found between 1137 and 1341

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