Mean of a normal distribution from two equal tail probabilities by symmetry, its standard deviation, and the probability of exceeding a value

The diagram shows the normal curve of a random variable \(Y\) with mean \(\mu\) and standard deviation \(\sigma\). It is given that \(\mathrm{P}(Y\le23)=0.05\).

1. The shaded region \(R\) lies under the curve where \(y\le23\). Write down the area of \(R\).[1]
2. It is also given that \(\mathrm{P}(Y\ge35)=0.05\). Find the value of \(\mu\), explaining your reasoning fully.[5]
3. Show that \(\sigma=3.65\), correct to three significant figures.[5]
4. Find \(\mathrm{P}(Y\ge31)\).[5]