Consider three observations a, b and c such that b = a + c. If the standard deviation of a + 2, b + 2, c + 2 is d, then which of the following is true ?
(1) \(b^2=3(a^2 + c^2) + 9d^2\)
(2) \(b^2=a^2 + c^2 + 3d^2\)
(3) \(b^2=3(a^2 + c^2 + d^2)\)
(4) \(b^2=3(a^2 + c^2) - 9d^2\)