A statistics professor gives a test and finds that the scores are normally distributed with a mean of 40 and a standard deviation of 10. She plans to curve the scores.
a. If she curves by adding 35 to each grade, what is the new mean? What is the new standard deviation?
b. Is it fair to curve by adding 35 to each grade? Why or why not?
c. If the grades are curved so that grades of B are given to scores above the bottom 70% and below the top 10%, find the numerical limits for a grade of B.
d. Which method of curving the grades is fairer: Adding 35 to each original score or using a scheme like the one given in part (c)? Explain.