Question

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a) 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 25 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 25.4, but not a 24.42.)

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

Letter	Scheme	Interval
A	Top 10%
B	Scores above the bottom 65% and below the top 10%
C	Scores above the bottom 35% and below the top 35%
D	Scores above the bottom 10% and below the top 65%
F	Bottom 10%

b) A teacher informs his organic chemistry 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 28 and a standard deviation of 5.7. 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 28.3, but not a 27.68.)

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

Letter	Scheme	Interval
A	Top 7%
B	Scores above the bottom 75% and below the top 7%
C	Scores above the bottom 25% and below the top 25%
D	Scores above the bottom 7% and below the top 75%
F	Bottom 7%

Answer 1

a)

A) for top 10 % ; z =1.28 ; hence score =mean +z*std deviation=34.3 grade A : score >34.3

B)for bottom 65% ; z =0.39 hence score =mean +z*std deviation=27.8 grade B : 27.8 <score <34.3

C)for 35% ;z =-0.39 ; hence score =mean +z*std deviation=22.2 ; grade C : 22.2 <score <27.8

d)

for bottom 10% ; z =-1.28 ;score =15.7 ; grade D : 15.7<score <22.2

F)

grade F score<15.7

b)

for top 7% ;z =1.48 ; grade A: score >36.4

for bottom 75% ; z =0.67 ; grade B : 31.8 < score<36.4

for bottom 25% ; z =-0.67 grade C : 24.2< score<31.8

for bottom 7% ; z =-1.48 ; grade D :19.6 < score <24.2

grade F: score <19.6