There are two major tests of readiness for college the ACT a

There are two major tests of readiness for college: the ACT and the SAT. ACT scores are reported on a scale from 1 to 36. The distribution of ACT scores in recent years has been roughly Normal with mean = 20.9 and standard deviation = 4.8. SAT scores are reported on a scale from 400 to 1600. SAT scores have been roughly Normal with mean = 1026 and standard deviation = 209.

The SAT scores that make up the top 12% of all scores range from (    ) to 1600.
(Round your answer to the nearest whole number.)

Solution

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.88      
          
Then, using table or technology,          
          
z =    1.174986792      
          
As x = u + z * s / sqrt(n)          
          
where          
          
u = mean =    1026      
z = the critical z score =    1.174986792      
s = standard deviation =    209      
          
Then          
          
x = critical value =    1271.57224 = 1272 [ANSWER]