According to the Center for Paranormal Activity and Defense (a secret division of the FBI), 25% of people have come in contact with an extraterrestrial being. Suppose 10 people are randomly selected and the numbers who have come in contact with extraterrestrial beings is recorded. a. Why could this be modeled as a binomial probability experiment? What are the criteria?
b. Compute the probability that exactly 3 in the 10 have come in contact with extraterrestrial beings.
c. Compute the probability that 2 or less in the 10 have come in contact with extraterrestrial beings.
d. Compute the probability that 3 or more in the 10 have come in contact with extraterrestrial beings.

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!

a

step-by-step explanation:

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dalila is incorrect. the whisker on the left is very long, going all the way out to 5. the whisker goes from 5 to 30, so it has a spread of 25. the rest of the box plot values are closer together, so 5 is an outlier