Coughlin et al estimated the percentage of women living in b

Coughlin et al. estimated the percentage of women living in border counties along the southern United States with Mexico (designated counties in California, Arizona, New Mexico, and Texas) who have less than a high school education to be 18.7. Assume the corresponding probability is .19. Suppose we select three women at random. Find the probability that the number with less than a high-school education is:

a. Exactly zero

b.More than one

c. Two or fewer

d. exactly three

Solution

probability of less then high school = 0.19

hence more then high school = 1-0.19 = 0.81

a) exactly 0 = p(x=0) = 3C0*(0.19)^0*(0.81)^3 = 0.531

B) P(X>1) = P(X=2) + P(X=3) = 3C2*(0.19)^2*(0.81) + 3C3*(0.19)^3*(0.81)^0 = 0.087 + 0.006 = 0.0093

C)P(X<=2) = 1 - p(X=3) = 1 - 0.006 = 0.994

D) (P=3) =3C3*(0.19)^3*(0.81)^0 = 0.006