Arandom sample of n = 64 observations is drawn from a population with a mean equal to 20 and standard deviation equal to 16. (give answers to four decimal places.) a) give the mean and standard deviation of the (repeated) sampling distribution of x. mean = standard deviation = b) calculate the standard normal z-score corresponding to a value of x = 16. c) calculate the standard normal z-score corresponding to a value of x = 23. d) find p(x < 16). e) find p(x > 23). f) find p(16 < x < 23).

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!

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maybe showing the graph would

step-by-step explanation:

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