At a certain excavation site, archaeological studies have used the method of tree-ring dating in an effort to determine when people lived in there. wood from several excavations gave a mean of (year) 619 with a standard deviation of 42 years. the distribution of dates was more or less mound-shaped and symmetrical about the mean. use the empirical rule to estimate a range of years centered about the mean in which about 99.7% of the data (tree-ring dates) will be found.

The range of years would be 493 to 745.

According to the empirical rule, 99.7% of data will fall within 3 standard deviations from the mean. Using this information, we have

619+3(42) and 619-3(42)
619+126 and 619-126
745 and 493

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MrRoyal MrRoyal · Answer 2 · 2022-06-29T15:00:32+02:00

The range of years centered about the mean in which about 99.7% of the data (tree-ring dates) will be found at 493 to 745 years

How to determine the range?

The given parameters are:

[tex]\bar x = 619[/tex] --- mean

[tex]\sigma = 42[/tex] --- standard deviation

In a normal distribution, the empirical rule states that 99.7% of data is at 3 standard deviations of the mean.

So, the range is calculated as:

[tex]Range = \bar x \pm 3\sigma[/tex]

This gives

[tex]Range = 619 \pm 3* 42[/tex]

Evaluate the product

[tex]Range = 619 \pm 126[/tex]

Expand

Range = (619 - 126, 619 + 126)

Evaluate

Range = (493, 745)

Hence, the range is 493 to 745