The distance achieved in a long jump competition by students at a school is normally distributed with mean 3.8 metres and standard deviation 0.9 metres. Students who achieve a distance greater than 4.3 metres receive a medal. (a) Find the proportion of students who receive medals. (3) The school wishes to give a certificate of achievement or a medal to the $$\(80 \%\)$$ of students who achieve a distance of at least $$\(d\)$$ metres. (b) Find the value of $$\(d\)$$. (3) Of those who received medals, the $$\(\frac{1}{3}\)$$ who jump the furthest will receive gold medals. (c) Find the shortest distance, $$\(g\)$$ metres, that must be achieved to receive a gold medal. (4) A journalist from the local newspaper interviews a randomly selected group of 3 medal winners. (d) Find the exact probability that there is at least one gold medal winner in the group. (3)

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