Problems 7 through 13: Select and answer 3 problems. (12 points each). 7. At Hogwarts School of Witchcraft and Wizardry, Professor Snape was concerned about grade inflation. As such, Professor Snape has begun to recommend grading students based on relative performance (standardize grading). Students scoring within 1 standard deviation of the mean earn a C. To earn a B, the student must score more than 1 standard deviation above normal. To earn an A, the student must be truly exceptional, and score 2 standard deviations above normal, although this is quite unusual. a. Determine the letter grade for the following students in Professor Snape's Potions course (M = 4.35, = 1.125) and in Professor Gilderoy Lockheart's Defense Against the Dark Arts course (M = 5.625, S = 0.75). b. Also, determine the percentile rank for these students, and each student, identify which course he (or she) scored best in: Potions (Mean = 4.35, SD = 1.125) DADA (Mean = 5.625, SD = 0.75) Harry 3.9 7.2 Hermione 5.175 7.125 Neville 4.725 5.7 Ron 4.125 5.475