In a University exam with a large number of candidates the r

In a University exam with a large number of candidates, the results in a
certain subject are scaled so that the marks will be normally distributed
with mean 100 and standard deviation 20. Students in the top 15% of
the marks are awarded an A-grade; a B-grade is awarded to those in
the next 15% of the marks and a Pass is awarded to the top 80% of the
grades.
Determine the cut-o marks for an A-grade a B-grade and a Pass.

Solution

a)

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.85      
          
Then, using table or technology,          
          
z =    1.036433389      
          
As x = u + z * s,          
          
where          
          
u = mean =    100      
z = the critical z score =    1.036433389      
s = standard deviation =    20      
          
Then          
          
x = critical value =    120.7286678   [ANSWER, CUT OFF A GRADE]

**********************

b)

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.7      
          
Then, using table or technology,          
          
z =    0.524400513      
          
As x = u + z * s,          
          
where          
          
u = mean =    100      
z = the critical z score =    0.524400513      
s = standard deviation =    20      
          
Then          
          
x = critical value =    110.4880103   [ANSWER, CUT OFF B GRADE]

***************************

c)

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.2      
          
Then, using table or technology,          
          
z =    -0.841621234      
          
As x = u + z * s,          
          
where          
          
u = mean =    100      
z = the critical z score =    -0.841621234      
s = standard deviation =    20      
          
Then          
          
x = critical value =    83.16757533   [ANSWER, CUT OFF OF PASSING]