3. A company produces bags of a chemical, and it is concerned about impurity content. It is believed that the weights of impurities per bag 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 larger. How? 4. Scores on a test follow a normal distribution. What is the probability that a randomly selected student will achieve a score that exceeds the mean score by more than 1.5 standard deviations? 5. An economics test is taken by a large group of students. The test scores are normally distributed with mean 60, and the probability that a randomly chosen student receives a score less than 75 is 0.9332. Four students are chosen at random. What is the probability that at least one of them scores more than 80 points on this test