Suppose an exam had an average (mean) score of 55%

Question

Suppose an exam had an average (mean) score of 55% and a standard deviation of 15%.

Table 6.3 Curving Grades
A 1.5 standard deviations above the mean or higher
B 0.5 to 1.5 standard deviations about the mean
C within 0.5 standard deviation of the mean
D 0.5 to 1.5 standard deviations below the mean
F 1.5 standard deviation below the mean or lower


If the teacher curved grades using the bell curve as in Table 6.3, what score would be necessary to receive an "A"? How about a "B"? And how about a "C"?

(Fill in the blanks below and round your answers to 1 decimal place.)

We would need to get a score of at least ____% to receive an A.

We would need to get a score between ____% and ____% to receive a B.

We would need to get a score between ____% and ___% to receive a C.

Answer 1

Obtain a z-score chart

http://www.utdallas.edu/dept/abp/zscoretable.pdf

 

z = (X - μ) / σ, where X = score, μ = mean, σ = standard deviation

 

A.

1.5 = (X - 55) / 15

22.5 = X - 55

77.5 = X

 

An A grace is a score ≥ 77.5              This complies with the "at least."

 

B.

0.5 = (X - 55) / 15

7.5 = X - 55

62.50 = X

 

A B grade is 62.5 < score < 77.5       This complies with the "between."

 

C.

0 = (X - 55) / 15

0 = X - 55

55 = x

 

A C grade is 55 < score < 62.5

 

The remainder are done in the same manner

 

Answer 2

A GRADE 1.5 SD above the mean would give us: 55 + 1.5*15% = 77.5 at least.

 

B GRADE 0.5 -1.5 SD above the mean gives a range of  55 + 0.5*15% to 55 + 1.5*15% = 62.5 -77.5 We would probably have to say 62.5-77.4

 

C GRADE We would calculate 55 +/- 0.5*15% = 47.5 to 62.5, so probably 47.5 - 62.4