A random variable \(X\) is normally distributed with mean 4.2 and standard deviation 1.1. Find the probability that the sum of two randomly chosen values of \(X\) is greater than 10 .
Each candidate's overall score for an essay is calculated as follows. The mark for creativity is denoted by \(C\), the penalty mark for spelling errors is denoted by \(S\) and the overall score is defined by \(C - \frac { 1 } { 2 } S\). The variables \(C\) and \(S\) are independent and have distributions \(\mathrm { N } ( 29,105 )\) and \(\mathrm { N } ( 17,15 )\) respectively. Find the proportion of candidates receiving a negative overall score.