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 42 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 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.

(1204 ; 1288) ;

(1162 ; 1330) ;

(1120 ; 1372)

Step-by-step explanation:

Given that:

Mean, m = 1246 years

Standard deviation, s = 42 years

68% is within one standard deviation the mean ;

Therefore 68% equals ;

mean ± 1(standard deviation)

(1246 - 1(42)) ; (1246 + 1(42))

1204 ; 1288

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

95% is within two standard deviation of the mean ;

Therefore 95% equals ;

mean ± 2(standard deviation)

(1246 - 2(42)) ; (1246 + 2(42)

(1246 - 84) ; (1246 + 84)

(1162 ; 1330)

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.

About 99.7% which is within 3 standard deviations of the mean

99.7% is within 3 standard deviations of the mean ;

Therefore ;

mean ± 3(standard deviation)

(1246 - 3(42)) ; (1246 + 3(42))

(1120 ; 1372)

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet