An instructor informs her physics class that a test is very difficult, but the grades will be curved. Scores for the test are normally distributed with a mean of 25 and a standard deviation of 5.
a. If she curves by adding 50 to each grade, what is the new mean? What is the new standard deviation?
b. Is it fair to curve by adding 50 to each grade? Why or why not?
c. If the grades are curved according to the following scheme (instead of adding 50), find the numerical limits for each letter grade.
A: Top 10%
B: Scores above the bottom 70% and below the top 10%
C: Scores above the bottom 30% and below the top 30%
D: Scores above the bottom 10% and below the top 70%
F: Bottom 10%
d. Which method of curving the grades is fairer: Adding 50 to each grade or using the scheme given in part (c)? Explain.