Research has shown, rather controversially, that when a family consists of multiple children that are genetic offspring of the parents (Le. not adopted], that the eldest child generally has a higher IQ than later born children. In this question we consider data from the USA in families with two children. It was shown that the elder child has on average a 10 point higher IQ than the younger child. Suppose X1 denotes the IQ of the older child in a randomly selected fam- ily, and X2 is the IQ of the younger child. The data showed that the joint distribution of the IQs (Le. of Xand X2) is approximately bivariate nor- mal, with E011] = 11D, 130(2) = 100, VaXi] = 225, Var{X2) = 225, and Corr[X1, X2] = 0.80. (a) What is the probability that the older child has an IQ at least 15 points higher than the IQ of the younger child? [b] Suppose 5 families with 2 children are randomly selected from the USA population. What is the probability that the older child has an IQ at least 15 points higher than the IQ of the younger child for at least 3 out of the 5 families? (c) Suppose a family is to be randomly chosen, and suppose that