One method of grading tests that uses a normal curve gives students letter grades depending on the standard‐deviation interval above or below the mean that cont

Question

One method of grading tests that uses a normal curve gives students letter grades depending on the standard‐deviation interval above or below the mean that contains their score: a grade of
 
F for below −2 standard deviations
D for −2 to −1 standard deviation
C for −1 to +1 standard deviation
B for +1 to +2 standard deviation
A for above +2 standard deviations
 
In the following, use this grading system and the fact that on a test given to 200 students the mean score was 76 and the standard deviation was 7.
 
a. How many students received an F?
 
 

students
 
b. How many students received a grade below a C?
 
 

students
 
c. How many students received a grade above a C?

Answer 1

All you have to do is to find the probabilities for the various z scores.

 

if z is between -1 and + 1, then you should know that 68.27% of the data lies therein so # of C's ought to be 137 (rounded up).

 

for A, beyond z = 2, Probability is 1-0.97725 = 0.02275 so # As is 4.55 (just four or five).

 

Similar considerations should be done by you!