Question 3. "Normal Distribution" (12 marks) a) The purchasing department of the RCMP must order uniform hats for new recruits. Past experience tells the Purchasing Manager that the circumferences of officers' heads are approximately normally distributed with mean 22.8 inches and standard deviation 1.1 inches. What proportion of officers has big heads (i.e., exceeding 24.5 inches in circumference)? (6 points). lo state b) Now suppose that the final exam scores are normally distributed with a mean of 60 and a standard deviation of 20. The instructor wishes to give 20% A's, 30% B's and the rest C or lower. What final score should be the cutoff between A and B? (Notice that the percentage of students who get A score is 20%). (6 points). 4