Question

A teacher informs his cell biology 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 26 and a standard deviation of 9. 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 26.6, but not a 25.31.)

The grades are curved according to the following scheme. Find the numerical limits for each letter grade.
A - Top 8%
B - Scores above the bottom 75%
and below the top 8%
C - Scores above the bottom 25%
and below the top 25%
D - Scores above the bottom 8%
and below the top 75%
F - Bottom 8%

Answer 1

To find the numerical limits for each letter grade, we need to determine the corresponding z-scores for each grade. We can then convert these z-scores back into exam scores using the given mean and standard deviation.

Step-by-step explanation:

To find the numerical limits for each letter grade, we need to determine the corresponding z-scores for each grade. We can then convert these z-scores back into exam scores using the given mean and standard deviation. The z-score for the top 8% is approximately 1.4, the z-score for the bottom 8% is approximately -1.4, the z-score for the bottom 25% is approximately -0.67, and the z-score for the top 25% is approximately 0.67. Converting these z-scores back into exam scores gives us the following numerical limits for each letter grade:

• A: Scores above 26 + (1.4 * 9) = 39.6
• B: Scores above 26 + (-0.67 * 9) = 19.13 and below 26 + (1.4 * 9) = 39.6
• C: Scores above 26 + (-0.67 * 9) = 19.13 and below 26 + (0.67 * 9) = 31.03
• D: Scores above 26 + (-1.4 * 9) = 11.6 and below 26 + (0.67 * 9) = 31.03
• F: Scores below 26 + (-1.4 * 9) = 11.6