Question

Suppose the mean monthly internet bill in Boulder is $50 with a standard deviation of $25. Find the mean and standard deviation of annual internet expenditures Y . Say the person pays X dollars monthly, plus an initial setup fee of $100 at the beginning of the year when he/she moves in

Answer 1

Let x = monthly internet will y = initial setup cost z = annual internet expenditure so, z = 12x + y = a_1 x + a_2 Y (a_1 = 12, a_2 = 6)Also, E[x] = $ 50, U[x] = $(25 times 25) = $ 625 and E[y] = $100, U[Y] = 0 so, E[z] = Sigma a_1 E[x_1] = 12 E [x] + E[y] = 12[50] + 600 = $ 700 and v[z] = Sigma a_i^2 v[x_i] = 12^2 v[x] + 1^2 v[y] = 144 v[x] = $ 144(625) so, sigma[z] = squareroot v[z] = 12 times 25 = $ 300 so, E[z] = $ 700 and sigma[z] = $ 300