A teacher informs her intermediate accounting class (of 500+ students) that a te

Question

A teacher informs her intermediate accounting 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 49 and a standard deviation of 9.7. 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 49.7, but not a 48.72.)

The grades are curved according to the following scheme. Find the numerical limits for each letter grade.

Letter Scheme Interval A Top 12% B Scores above the bottom 75%
and below the top 12% C Scores above the bottom 25%
and below the top 25% D Scores above the bottom 12%
and below the top 75% F Bottom 12%

Explanation / Answer

Mean = 49

Standard deviation = 9.7

P(X < A) = P(Z < (A - mean) / standard deviation)

A) For top 12%, P(X < A) = 1 - 0.12 = 0.88

P(Z < (A - 49)/9.7) = 0.88

From standard normal distribution table,

(A - 49)/9.7) = 0.81

A = 56.9

So, the interval is 56.9 to 100

B) let B indicate the score above bottom 75%

P(X < B) = 0.75

P(Z < (B - 49)/9.7) = 0.75

(B - 49)/9.7 = 0.77

B = 56.5

Interval is 56.5 to 56.9

C) Let C indicate the score above bottom 25%

(C - 49)/9.7) = -0.77

C = 41.5

Interval is 41.5 to 56.5

D) Let D denote the score above bottom 12%

(D - 49)/9.7) = -0.81

D = 41.1

Interval = 41.1 to 41.5

E) Bottom 12% interval is 0 to 41.1

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