A kind of plant has only blue flowers and white flowers. According to a genetic theory, the offspring of a certain cross have a 75% chance to be blue-flowering and a 25% chance to be white-flowering, independently of one another. Two hundred seeds of such a cross are raised, and 142 turn out to be blue-flowering. Are the data consistent with the theory? Answer yes or no and explain. X = 1 <- blue X = 0 <- white X ~ Bernoulli(0.75) E(X) = p = 0.75 SD(X) = sqrt(p(1-p)) = sqrt(0.75*0.25) = 0.43 S = sum(X_k) S ~ Bin(0.75, 200) E(S) = Np = 200*0.75 = 150 SD(S) = sqrt(Np(1-p)) = sqrt(150*0.25) = sqrt(37.5) = 6.12 R = S/N E(R) = p = 0.75 SD(R) = SE(X) = 1/sqrt(N) * sqrt(p(1-p)) = SD(X)/sqrt(N) = 0.43/sqrt(200) = 0.030 z = (142 - 150)/200*SD(E) = 0.04/0.030 = 1.306 p = P[z >= 1.306] = 0.097