An often asked question after an question or test, will the grades be curved?. The usual meaning of the question is will the instructor add points to each students score to account for difficult questions or overall class performance. However, students have taken standardized tests throughout their school career. These standardized tests have performance normed so that over time, scores from year to year are comparable. What would it mean to norm or curve class scores using this philosophy instead of just adding points to each test score to improve performance for everyone in the class.

Dr. Smith an economics professor will test his students with a standardized test on Macro Economics that is nationally normed (think normal distribution here). Therefore, the normal distribution will approximate the distribution of student scores on the test. As such, the normed distribution has a mean = 78, and a standard deviation of 8.

1. Using the empirical rule, what would be the total range of scores for all students?

Maximum expected score _______________ Minimum expected score _____________

Dr. Smith initially decides to curve the class scores according to the following criteria relative to the normal distribution with mean = 78 and the standard deviation = 8. So instead of having the standard 90,80,70,60 and below 60 points he will use

• At or above the 90^th percentile = A
• At or above the 80^th percentile = B
• At or above the 70^th percentile = C
• At or above the 60^th percentile = D
• Below 60^th percentile = F

2. Given the above grading criteria, what are the standardized Z values for each minimum score for each grade A-F?

Grade	Standardized Z score
A
B
C
D
F

3. Based on the information above, what will be the actual point score ranges for each grade?

Point Grade	Minimum	Maximum
A		100
B
C
D
F

4. Below is a sample of the first 10 students to complete the exam. These are the raw point scores based on correct answers. Using the above table you just created, what would be the score if Dr. Smith were to curve the grades to this criteria?

Student	Raw Score in points/ letter grade	Curved Letter grade based on above criteria normed
Artie	82/B
Bubba	77/C
Shana	91/A
Tommy	86/B
Sallyanne	75/C
Louis	66/D
Earl	88/B
Marsha	69/D
Sarah	79/C
Alvin	81/B

5. After reviewing the above curved letter grades, Dr. Smith considers another curving method based on the normal distribution. The criteria is below.

• A: Scores that are at least 2 standard deviations above the mean of the standardized test.
• B: Scores that are from one up to two standard deviations of the mean standardized test.
• C: Scores that are from one standard deviation below the mean up to one standard deviation above the mean of the standardized test.
• D: Scores that are from two standard deviations below the mean up to one standard deviation below the mean of the standardized test.
• F: Scores that are below two standard deviations below the mean of the standardized test.

Complete the table below with the raw score letter grades according to the above criteria suggested by Dr. Smith.

Point Grade	Minimum	Maximum
A		100
B
C
D
F

6. Using the above letter grade criteria, assign grades to the ten students based on Dr. Smiths latest criteria.

Student	Raw Score in points/ letter grade	Curved Letter grade based on above criteria normed
Artie	82/B
Bubba	77/C
Shana	91/A
Tommy	86/B
Sallyanne	75/C
Louis	66/D
Earl	88/B
Marsha	69/D
Sarah	79/C
Alvin	81/B

7. Compare the letter grades awarded for the raw points scores using question 4 and question 6 curving schemes. Which curve grading scheme do you think is most fair? Why? Be concise and precise with your answer.