A history teacher assigns letter grades on a test according to the following scheme: A: Top 10% B: Scores below the top 10% and above the bottom 60% C: Scores below the top 40% and above the bottom 20% D: Scores below the top 80% and above the bottom 10% F: Bottom 10% Scores on the test are normally distributed with a mean of 69 and a standard deviation of 13.4. Find the numerical limits for each letter grade.

A) A: Above 86
B: Between 72 and 86
$ C $ : Between 58 and 71
D: Between 52 and 57
F: Below 52

B) A: Above 81
B: Between 72 and 81
$ C $ : Between 58 and 71
D: Between 52 and 57
F: Below 52

C) A: Above 86
B: Between 76 and 86
C: Between 58 and 75
D: Between 52 and 57
F: Below 52

D) A: Above 81
B: Between 72 and 81
C: Between 58 and 71
D: Between 54 and 57
F: Below 54

Question

A history teacher assigns letter grades on a test according to the following scheme: A: Top 10% B: Scores below the top 10% and above the bottom 60% C: Scores below the top 40% and above the bottom 20% D: Scores below the top 80% and above the bottom 10% F: Bottom 10% Scores on the test are normally distributed with a mean of 69 and a standard deviation of 13.4. Find the numerical limits for each letter grade.

A) A: Above 86
B: Between 72 and 86
$ C $ : Between 58 and 71
D: Between 52 and 57
F: Below 52

B) A: Above 81
B: Between 72 and 81
$ C $ : Between 58 and 71
D: Between 52 and 57
F: Below 52

C) A: Above 86
B: Between 76 and 86
C: Between 58 and 75
D: Between 52 and 57
F: Below 52

D) A: Above 81
B: Between 72 and 81
C: Between 58 and 71
D: Between 54 and 57
F: Below 54

Quizplus · Accepted Answer

To find the numerical limits for each letter grade, we use the Z-score formula $Z = \frac{X - \mu}{\sigma}$, where $X$ is the score, $\mu$ is the mean, and $\sigma$ is the standard deviation. For a normally distributed set of scores, the top 10% corresponds to a Z-score of approximately 1.28, the top 40% to a Z-score of approximately 0.25, the bottom 60% (or top 40%) to a Z-score of approximately -0.25, the top 80% to a Z-score of approximately -0.84, and the bottom 10% to a Z-score of approximately -1.28. Using these Z-scores and the given mean (69) and standard deviation (13.4), we calculate the score limits for each grade category. For example, for A (top 10%), the score limit is $69 + 1.28(13.4) \approx 86$. Similar calculations for other grades lead to the limits provided in option A.

A History Teacher Assigns Letter Grades on a Test According C C C

A History Teacher Assigns Letter Grades on a Test According $C$