A company produces bags of a chemical, and it is concerned about impurity content. It is believed that the weights of impurities per bug are normally distributed, with mean 12.2 grams, and standard deviation 2.8 grams. A bag is chosen at random.

(a) What is the probability that it contains less than 10 grams of impurities?

(b) What is the probability that it contains more than 15 grams of impurities?

(c) What is the probability that it contains between 12 and 15 grams of impurities?

(d) It is possible, without doing the detailed calculations, to deduce which of the answers to

(a) and

(b) will be the larger. How?