A teacher informs her computational physics class (of 500+ students) that a test

Question

A teacher informs her computational physics 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 27 and a standard deviation of 7.3. 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 27.8, but not a 26.34.)

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

Letter Scheme Interval A Top 8% B Scores above the bottom 67%
and below the top 8% C Scores above the bottom 33%
and below the top 33% D Scores above the bottom 8%
and below the top 67% F Bottom 8%

Explanation / Answer

for top 8% ; z =1.41 ; hence corresponding score =mean+z*std deviaiton =37.3 ; grade A : score >37.3

for 67% z =0.44 ;  hence corresponding score =mean+z*std deviaiton =30.2 ; grade B: 30.2 < score <37.3

for 33% ; z =-0.44;corresponding score =mean+z*std deviaiton =23.8 ; grade C:23.8 < score <30.2

for 8%; z =-1.41;corresponding score =mean+z*std deviaiton =16.7; grade D : 16.7 < scre< 23.8

grade F : score <16.7

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