Southwest Co-op produces bags of fertilizer, and it is concerned about impurity content. It is believed that the weights of impurities per bag are normally distributed with a mean of 12.2 grams and a standard deviation of 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 parts (a) and (b) will be the larger. How would you do this?