In a sample of 138 tables, the average height was found to be 34.3in. with a variance of 0.7. Give a point estimate for the population variance of the height of the tables. Round your answer to two decimal places, if necessary.

0.70.

Step-by-step explanation:

Given : For the sample of  138 tables, the average height was found to be 34.3in. with a variance of 0.7.

It means the sample variance  () is 0.70.

Since , we know that the sample variance is the best point estimate of the population variance in a statistical study.

Therefore ,  a point estimate for the population variance of the height of the tables would be 0.70.

Hence, the correct answer is 0.70.

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

step-by-step explanation:

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