Question

A teacher informs his psyhcology class (of 500+ students) that a test was very difficult, but the grades would be curved. Scores on the test were normally distributed with a mean of 28 and a standard deviation of 9.2. The maximum possible score on the test was 100 points. Because of partial credit, scores were recorded with 1 decimal point accuracy. (Thus, a student could earn a 28.3, but not a 27.33.) The grades are curved according to the following scheme. Find the numerical limits for each letter grade. Letter Scheme Interval A Top 11% B Scores above the bottom 68% and below the top 11% C Scores above the bottom 32% and below the top 32% D Scores above the bottom 11% and below the top 68% F Bottom 11%

Answer 1

A-Top 11% : The z score with a left tail of 0.89,

z=invNorm(0.89) = 1.227

The corresponding score, x = z*s + u = 1.227*9.2 + 28 = 39.3

B-Scores above bottom 68% and below top 11% : between scores invNorm(.68)*9.2+28 and 39.3

= between 32.3 and 39.3

C- Scores above bottom 32% and below top 32% : between scores invNorm(.32)*9.2+28 and 32.3    = between 23.7 and 32.3

D- Scores above bottom 11% and below top 68% : between scores invNorm(.11)*9.2+28 and 23.7    = between 16.7 and 23.7

F- Bottom 11% : between scores 0 and 16.7