The average IQ of soldiers is 96 with a standard deviation 1

The average IQ of soldiers is 96 with a standard deviation 16 points. what is the probability to have 35 soldiers of IQ > 98 points? (Use sampling theory)

Solution

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    98      
u = mean =    96      
n = sample size =    35      
s = standard deviation =    16      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    0.739509973      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   0.739509973   ) =    0.229798693 [ANSWER]