The grades assigned to students taking a midterm in a large principles of economics class is assumed to be normally distributed with a mean of 75 and a standard deviation of 7. The Professor teaching the class, known to be a "stringent grader", has indicated that based on this distribution of grades, she intends to "grade on the curve", whereby the top 15 percent of the students will receive A's, the next 20 percent will receive B's, the "middle" 30 percent will receive \(C^{\prime}\) 's, the next 20 percent will receive D's, and finally, the lowest 15 percent will receive F's.

(a) Derive the grade ranges associated with each of the letter grades that will be assigned in the class.

(b) Can the grade distribution actually be normally distributed in this case, or must the normal distribution be only an approximation? Explain.