Solutions HWA02

8.14:

z_{.25} = -0.6745, so x_{.25} = 167 + (-0.6745)(30) = 146.8

z_{.90} = +1.2815, so x_{.90} = 167 + (1.2815)(30) = 205.4

z_{.95} = +1.6449, so x_{.25} = 167 + (1.6449)(30) = 216.3

8.24a: Normal approximation with continuity correction. Here pi = 1/6, mu = (36)(1/6) = 6, sigma = sqrt[(36)(1/6)(5/6)] = 2.2361

Pr(4 <= K <= 10) =(C.C.) Pr(3.5 < K < 10.5) =(N.A.) Pr (-1.12 < Z < 2.01) = .8461

8.24b: Exact probability. Pr(4 <= K <= 10) = (36 take 4)(1/6)^4(5/6)^32 + (36 take 5)(1/6)^5(5/6)^31+ (36 take 6)(1/6)^6(5/6)^30 + (36 take 7)(1/6)^7(5/6)^29 + (36 take 8)(1/6)^8(5/6)^28 + (36 take 9)(1/6)^9(5/6)^27 + (36 take 10)(1/6)^10(5/6)^26 = binomcdf(36,1/6,10) – binomcdf(36,1/6,3) = .9715 - .1277 = .8438

8.36a: Pr(X > 7 ) = Pr(z > (7-6.4)/0.3) = .0228

8.36b: Pr(X < 6 ) = Pr(z < (6-6.4)/0.3) = .0912