Scores obtained on a particular aptitude test by psychology

Scores obtained on a particular aptitude test by psychology students are normally distributed, with a mean of 150 and a standard deviation of 25. Assume the distribution is a population set of scores. What percentage of scores are below a score of 105?

Solution

a)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    105      
u = mean =    150      
          
s = standard deviation =    25      
          
Thus,          
          
z = (x - u) / s =    -1.8      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -1.8   ) =    0.035930319 or 3.5930319%  [ANSWER]