Scores on a national statistical test are normally distribut

Scores on a national statistical test are normally distributed with a mean of 83.3 and a standard deviation of 4. If a random sample of 16 tests were taken, what is the probability that the sample mean will be greater than 85?

Solution

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    85      
u = mean =    83.3      
n = sample size =    16      
s = standard deviation =    4      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    1.7      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   1.7   ) =    0.044565463 [ANSWER]