4 A company that makes meat pies includes a "small" size in its product range. These pies consist of a pastry case and meat filling, the weights of which are independent of each other. The weight of the pastry case, \(C\), is Normally distributed with mean 96 g and variance \(21 \mathrm {~g} ^ { 2 }\). The weight of the meat filling, \(M\), is Normally distributed with mean 57 g and variance \(14 \mathrm {~g} ^ { 2 }\).

1. Find the probability that, in a randomly chosen pie, the weight of the pastry case is between 90 and 100 g .
2. The wrappers on the pies state that the weight is 145 g . Find the proportion of pies that are underweight.
3. The pies are sold in packs of 4 . Find the value of \(w\) such that, in \(95 \%\) of packs, the total weight of the 4 pies in a randomly chosen pack exceeds \(w \mathrm {~g}\).
4. It is required that the weight of the meat filling in a pie should be at least \(35 \%\) of the total weight. Show that this means that \(0.65 M - 0.35 C \geqslant 0\). Hence find the probability that, in a randomly chosen pie, this requirement is met.