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 .
Estimate the proportion of letters sent by the company that weigh less than 120 g .
Kris splits the letters to be sent into 3 categories: heavy, medium and light, with \(\frac { 1 } { 3 }\) of the letters in each category.
Find the weight limits that determine medium letters.
A heavy letter is chosen at random.
Find the probability that this letter weighs less than 200 g .
Kris chooses a random sample of 3 letters from those in the mailroom one day.
Find the probability that there is one letter in each of the 3 categories.