Kris works in the mailroom of a large company and is responsible for all the letters sent by the company. The weights of letters sent by the company, $$\(W\)$$ grams, have a normal distribution with mean $$\(165 \mathrm{~g}\)$$ and standard deviation $$\(35 \mathrm{~g}\)$$. (a) Estimate the proportion of letters sent by the company that weigh less than $$\(120 \mathrm{~g}\)$$. (3) Kris splits the letters to be sent into 3 categories: heavy, medium and light, with $$\(\frac{1}{3}\)$$ of the letters in each category. (b) Find the weight limits that determine medium letters. (4) A heavy letter is chosen at random. (c) Find the probability that this letter weighs less than $$\(200 \mathrm{~g}\)$$. (3) Kris chooses a random sample of 3 letters from those in the mailroom one day. (d) Find the probability that there is one letter in each of the 3 categories. (3)

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