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) $b ^ { 2 } = 3 \left( a ^ { 2 } + c ^ { 2 } \right) + 9 d ^ { 2 }$\\
(2) $b ^ { 2 } = a ^ { 2 } + c ^ { 2 } + 3 d ^ { 2 }$\\
(3) $b ^ { 2 } = 3 \left( a ^ { 2 } + c ^ { 2 } + d ^ { 2 } \right)$\\
(4) $b ^ { 2 } = 3 \left( a ^ { 2 } + c ^ { 2 } \right) - 9 d ^ { 2 }$