Question

A statistics instructor has decided to grade on a curve that results in the following distribution: A’s – top 10% of students; B’s – next 20% of students; C’s – middle 40% of students ; D’s – next 20% of students; F’s – bottom 10% of students .   If the exam has a mean grade of 75 with a standard deviation of 15, what exam scores would border each letter grade (provide answers to the nearest integer)? A's would be students with scores above B's would be grades above and up to   C's would be grades above and up to   D's would be grades above and up to   F's would be grades at or below   What exam scores would border each letter grade if the exam had a mean of 80 with a standard deviation of 5 (provide answers to the nearest integer)? A's would be students with scores above B's would be grades above and up to   C's would be grades above and up to   D's would be grades above and up to   F's would be grades at or below   Is grading on a curve always a benefit to every student? Who do you think it benefits and when?

Answer 1

Solution:

If the exam has a mean grade of 75 with a standard deviation of 15, what exam scores would border each letter grade (provide answers to the nearest integer)?

We know that exam scores are normally distributed.

We are given

Mean = 75

SD = 15

For top 10% students, Z = 1.281551566

(by using z-table or excel)

Note, all z-scores in the next calculations are calculated by using either excel or z-table.

X = Mean + Z*SD

X = 75 + 1.281551566*15

X = 94.22327349

A's would be students with scores above 94.

B’s – next 20% of students;

Z = 0.524400513

X = Mean + Z*SD

X = 75 + 0.524400513*15

X = 82.8660077

B's would be grades above 83 and up to 94.

C’s – middle 40% of students;

Z = -0.524400513

X = Mean + Z*SD

X = 75 + (-0.524400513)*15

X = 67.13399231

C's would be grades above 67 and up to 83.

D’s – next 20% of students;

Z = -1.281551566

X = 75 + (-1.281551566)*15

X = 55.77672651

D's would be grades above 56 and up to 67.

F's would be grades at or below 56.

What exam scores would border each letter grade if the exam had a mean of 80 with a standard deviation of 5 (provide answers to the nearest integer)?

We are given

Mean = 80

SD = 5

For top 10% students, Z = 1.281551566

X = Mean + Z*SD

X = 80 + 1.281551566*5

X = 86.40775783

A's would be students with scores above 86.

B’s – next 20% of students;

Z = 0.524400513

X = Mean + Z*SD

X = 80 + 0.524400513*5

X = 82.62200257

B's would be grades above 83 and up to 86.

C’s – middle 40% of students;

Z = -0.524400513

X = Mean + Z*SD

X = 80 + (-0.524400513)*5

X = 77.37799744

C's would be grades above 77 and up to 83.

D’s – next 20% of students;

Z = -1.281551566

X = 80 + (-1.281551566)*5

X = 73.59224217

D's would be grades above 74 and up to 77.

F's would be grades at or below 74.

Is grading on a curve always a benefit to every student? Who do you think it benefits and when?

No, grading on a curve do not always a benefit to every student. If the standard deviation is less, then it is not so much benefit, but when standard deviation is more, then it would be beneficial to students with comparatively less score.