Delivery time under two probability requirements

The total delivery time \(T\), in seconds, follows the distribution \(T\sim N(1800,225+\sigma^2)\), where \(\sigma>0\).

1. Given that \(\sigma=40\), find \(P(1680<T<1920)\).[2]
2. The delivery company requires the delivery time to differ from its mean by less than \(120\) seconds with probability at least \(0.90\). Find the greatest possible value of \(\sigma\).[4]
3. The company introduces the additional requirement that \(P(T>1900)\leq0.05\). Find the range of values of \(\sigma\) for which both requirements are satisfied.[4]