A student scores 91 on the midterm exam for physics Assume t

A student scores 91 on the midterm exam for physics. Assume the class scores are normally distributed, with a mean of 65 and standard deviation of 15. Into what percentile does this student fall?

Solution

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    91      
u = mean =    65      
          
s = standard deviation =    15      
          
Thus,          
          
z = (x - u) / s =    1.733333333      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   1.733333333   ) =    0.95848178 or 95.85th percentile [ANSWER]