Professor Gauss assumes that students' final grade scores in his class are the value of normally distributed random variable. Suppose Prof. Gauss defines his grading scale as follows: 1. grade A to those students whose score exceeds + o 2. grade B to those students whose score falls between and u+o 3. grade C if a score falls between - and u 4. grade D if a score falls between -30 and - 20 5. and an F grade if a score falls below -30 a) Compute the proportions of students receiving each grade as listed in parts (1) to (5). Please show your work. b) Now use empirical rule (or 68-95-99.7 rule) to find the approximate proportions in cases (1) to (5) above. How close are the approximate proportions to the exact values? a

Professor Gauss assumes that students' final grade scores in his class are the valae of followst 1. Irade A to those students whose score excecds +. 2. grade B to those students whose score falls between at d+a 4. grade D If nscorefalls between 30 and 20 5. and an F grade if a score falls below 3a a) Compute the proportions of students receiving each prode as listed in parts (1) to (5) Please show your work b) Now use empirical rule (or 689599,7 rule) to find the approxumate proportions in: cases (1) to (5) above. How close are the approximate propottions to the cact whire