Use normal symmetry and tail quantiles to determine mean, standard deviation and a cumulative probability.

The graph shows a normal curve for the random variable \(X\), with mean \(\mu\) and standard deviation \(\sigma\). It is known that \(P(X\ge12)=0.1\).

1. The shaded region \(A\) is the region under the curve where \(x\ge12\). Write down the area of the shaded region \(A\).[1]
2. It is also known that \(P(X\le8)=0.1\). Find the value of \(\mu\), explaining your method in full.[5]
3. Show that \(\sigma=1.56\) to an accuracy of three significant figures.[5]
4. Find \(P(X\le11)\).[5]