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 g and standard deviation 35 g. (a) Estimate the proportion of letters sent by the company that weigh less than 120g. (3) Kris splits the letters to be sent into 3 categories: heavy, medium and light, with 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 200g. (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.