(a) Explain what you understand by the sampling distribution of a statistic. (1) A factory produces beads in bags for craft shops. A small bag contains 40 beads, a medium bag contains 80 beads and a large bag contains 150 beads. The factory produces small, medium and large bags in the ratio 5:3:2 respectively. A random sample of 3 bags is taken from the factory. (b) Find the sampling distribution for the range of the number of beads in the 3 bags in the sample. (7) A random sample of $$\(n\)$$ sets of 3 bags is taken. The random variable $$\(Y\)$$ represents the number of these $$\(n\)$$ sets of 3 bags that have a range of 70 (c) Calculate the minimum value of $$\(n\)$$ such that $$\(\mathrm{P}(Y=0)< 0.2\)$$ (3)

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