Define a random variable Y to be Y = X1 + X2 + · · · + Xn n , where n is a fixed positive constant number. Suppose all of the X’s follow the same normal distribution, each with the same mean µ and the same variance σ 2 , so X1 ∼ N(µ, σ2 ); X2 ∼ N(µ, σ2 ); . . . ; Xn ∼ N(µ, σ2 ). Suppose that all of the X’s are independent. (a) Find E(Y ) = E X1 + X2 + · · · + Xn n . (b) Find V(Y ) = V X1 + X2 + · · · + Xn n

Grace is standing 18 feet from a lighthouse and kelly is standing 10 feet from grace. the angle that grace looks up to see the top of the lighthouse is 45°. the angle that kelly looks up to see the top of the lighthouse is y°. find the height, h, of the lighthouse. find the angle, rounded to the nearest tenth of a degree, in which kelly looks up to the top of the lighthouse. to the nearest tenth of a degree, find the value of x° . in two or more sentences, explain your calculations