Professor uses a normal distribution to assign grades in his class. He assigns an A to students scoring more than 2 standard deviations above the mean and a F to students scoring more than two standard deviations below the mean. He assigns a B to students who score between 1 and 2 standard deviations above the mean and a D to students who score 1and 2 standard deviations below the mean. All other students get a C. What percent of the class receives each grade assuming the scores are normally distributed? Show all calculations.

Please input formula use for the solution and detailed work