a college administrator states that the average high school

a college administrator states that the average high school GPA for incoming freshman students is normally distributed with a mean equal to 3.30 and a standard deviation equal to 0.20. If studenta with a GPA in the top 10% will be offered a scholarship then what is the minimum GPA required to receive the scholarship?

Solution

First, we get the z score from the given left tailed area. As          
          
Left tailed area = 1 - 0.10 =    0.9      
          
Then, using table or technology,          
          
z =    1.281551566      
          
As x = u + z * s,          
          
where          
          
u = mean =    3.3      
z = the critical z score =    1.281551566      
s = standard deviation =    0.2      
          
Then          
          
x = critical value =    3.556310313   [ANSWER]