Please provide full explanation There are two major tests of

Please provide full explanation

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 25 % of all scores range from __________? to 1600.

Solution

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.75      
          
Then, using table or technology,          
          
z =    0.67448975      
          
As x = u + z * s / sqrt(n)          
          
where          
          
u = mean =    1026      
z = the critical z score =    0.67448975      
s = standard deviation =    209      
          
Then          
          
x = critical value =    1166.968358

Hence, The SAT scores that make up the top 25 % of all scores range from 1166.968358 to 1600.