Suppose ACT Reading scores are normally distributed with a m

Suppose ACT Reading scores are normally distributed with a mean of 21.2 and a standard deviation of 6.2. A university plans to award scholarships to students whose scores are in the top 6%. What is the minimum score required for the scholarship? Round your answer to the nearest tenth, if necessary.

Solution

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.94      
          
Then, using table or technology,          
          
z =    1.554773595      
          
As x = u + z * s,          
          
where          
          
u = mean =    21.2      
z = the critical z score =    1.554773595      
s = standard deviation =    6.2      
          
Then          
          
x = critical value =    30.83959629 = 30.8 [ANSWER]