Question

The combined math and verbal scores for females taking the SAT-I test are normally distributed with a mean of 998 and a standard deviation of 202 (based on date from the College Board). If a college includes a minimum score of 1100 among its requirements, what percentage of females do not satisfy that requirement?

Answer 1

Let X be the combined SAT scores                  
X follows normal distribution mean μ and standard deviation σ                  
Given    μ = 998       σ = 202      
Since minimum score is 1100                  
Percentage of females not satisfying the score is given by                  
P(X < 1100)                  
Converting to z-scores                  
P(X < 1100) = P(Z < Z')                  
where                  
   
z-score = 0.51                  
P(X < 1100) = P(Z < 0.51)                  
Using standard normal tables we get P(Z < 0.51)                  
P(X < 1100) = P(Z < 0.51)                  
   = 0.6950              
Percentage of females do not satisfy that requirement = 69.50%