3. Let X1,X2,X3 be independent normal random variables with common mean 1 = 60 and common variance 2 1 = 12, and Y1,Y2,Y3 be independent

3. Let X1,X2,X3 be independent normal random variables with common mean μ1 = 60 and common variance

σ2 1 = 12, and Y1,Y2,Y3 be independent normal random variables with common mean μ2 = 65 and common variance

σ2 2 = 15. Also, Xi and Yj are independent for all i and j.

(a) Specify the distribution of X1 + X2 + X3, and find P(X1 + X2 + X3 > 185).

(b) Specify the distribution of Y −X, and find P(Y −X >8).