Each part has a distribution that is roughly unimodal and sy

Each part has a distribution that is roughly unimodal and symmetric and is designed o have an overall mean of about 500 and a standard deviation of 100 for all test takers. QUESTION - Suppose you earned a 700 on one part of your SAT where do you stand among all students who take that test?

Solution

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    700      
u = mean =    500      
          
s = standard deviation =    100      
          
Thus,          
          
z = (x - u) / s =    2      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   2   ) =    0.977249868

Hence, you are on the 97.72th percentile. [ANSWER]