7. As part of a selection procedure for a company, applicants have to answer all 20 questions of a multiple choice test. If an applicant chooses answers at random the probability of choosing a correct answer is 0.2 and the number of correct answers is represented by the random variable \(X\).

1. Suggest a suitable distribution for \(X\).
   (2) Each applicant gains 4 points for each correct answer but loses 1 point for each incorrect answer. The random variable \(S\) represents the final score, in points, for an applicant who chooses answers to this test at random.
2. Show that \(S = 5 X - 20\)
3. Find \(\mathrm { E } ( S )\) and \(\operatorname { Var } ( S )\). An applicant who achieves a score of at least 20 points is invited to take part in the final stage of the selection process.
4. Find \(\mathrm { P } ( S \geqslant 20 )\)
   (4) Cameron is taking the final stage of the selection process which is a multiple choice test consisting of 100 questions. He has been preparing for this test and believes that his chance of answering each question correctly is 0.4
5. Using a suitable approximation, estimate the probability that Cameron answers more than half of the questions correctly.