Problems 1 through 13: Select and answer 3 problems. {1.2 points each}. I". At Hogwarts School of Witchcraft and Wizardry, Professor Snap-e was concerned about grade ination. rs 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 E, the student must score more than 1 standard deviation above normal. To earn an A, the student must be trulyr 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 II23ilrlero3r [ockheart's Defense Against the Dani: Arts course [M = 1&5, .5'. = on}. b. Also, determine the percentile rank for them students, and each student, identifyr which course he (or she] scored best in: Potions can = 4.35, so = 1.125 neon Mean = 5.625, so = ots