3 The scores, \(X\), in Paper 1 of an English examination have an underlying Normal distribution with mean 76 and standard deviation 12. The scores are reported as integer marks. So, for example, a score for which \(75.5 \leqslant X < 76.5\) is reported as 76 marks.

1. Find the probability that a candidate's reported mark is 76 .
2. Find the probability that a candidate's reported mark is at least 80 .
3. Three candidates are chosen at random. Find the probability that exactly one of these three candidates' reported marks is at least 80 . The proportion of candidates who receive an A* grade (the highest grade) must not exceed \(10 \%\) but should be as close as possible to \(10 \%\).
4. Find the lowest reported mark that should be awarded an A* grade. The scores in Paper 2 of the examination have an underlying Normal distribution with mean \(\mu\) and standard deviation 12.
5. Given that \(20 \%\) of candidates receive a reported mark of 50 or less, find the value of \(\mu\).