Fulltime PhD students receive an average of 12837 per year w

Full-time Ph.D. students receive an average of $12,837 per year with a standard deviation of $3000. Find the probability that the average salary of a group of 16 randomly selected Ph.D. students is more than $13,000.

Solution

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    13000      
u = mean =    12837      
n = sample size =    16      
s = standard deviation =    3000      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    0.217333333      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   0.217333333   ) =    0.413974291 [ANSWER]