18. Variance = s2 = E(x2 ) ñ µ2 , where E(x2 ) = Sx2 p(x) = 1(1) + 4(.2) + 9(.2) + 16(.4) + 25(.1) =

18. Variance = s2 = E(x2 ) ñ µ2 , where E(x2 ) = Sx2 p(x) = 1(1) + 4(.2) + 9(.2) + 16(.4) + 25(.1) = 11.6 Hence s2 = 11.6 ñ 3.22 = 1.36. The answer is (D). 19. The number of voters in the city has a binomial distribution with n = 40 and p = .8. Hence the mean is µ = np = 40(.8) = 32. The answer is (C). 20. P(x > 56.5) = P(z > [56.5 ñ 50]/10) = P(z > 0.65). Go the z-table to look up 0.65. One finds .2422. This is the area between 0 and 0.65. Since we need the area to the right of 0.65, we find the probability as 0.5 ñ 0.2422 = .2578. The answer is (A). 21. P(x < 45) = P(z < [45 ñ 50]/10) = P(z < ñ0.5). Go to the z-table to look up 0.5. One finds .1915. This is the area between 0 and ñ0.5. Since we need the area to the left of ñ0.5, we find the probability as 0.5 ñ 0.1915 = 0.3085. The answer is (D).