Krishi owns a farm on which he keeps chickens. He selects, at random, 10 of the eggs produced and weighs each of them. You may assume that these weights are a random sample from a normal distribution with standard deviation $$\(1.9 \mathrm{~g}\)$$ The total weight of these 10 eggs is $$\(537.2 \mathrm{~g}\)$$ Find a 95\% confidence interval for the mean weight of the eggs produced by Krishi's chickens. (4) Krishi was hoping to obtain a 99\% confidence interval of width at most $$\(1.5 \mathrm{~g}\)$$

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