5 Gem stones from a certain mine have weights, \(X\) grams, which are normally distributed with mean 1.9 g and standard deviation 0.55 g . These gem stones are sorted into three categories for sale depending on their weights, as follows. Small: under 1.2 g Medium: between 1.2 g and 2.5 g Large: over 2.5 g

1. Find the proportion of gem stones in each of these three categories.
2. Find the value of \(k\) such that \(\mathrm { P } ( k < X < 2.5 ) = 0.8\).