The average height of US adult males is 695 in and the stand

The average height of U.S. adult males is 69.5 in. and the standard deviation is 2.0. A physician thinks that this national mean seems a little short for his patients, so he records the height of the next 100 adult males to visit his office. Their average height is 69.75 in. If this physician\'s adult male patients are just a representative sample of nationwide adult males, what is the probability that his patients were so tall?

Solution

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    69.75      
u = mean =    69.5      
n = sample size =    100      
s = standard deviation =    2      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    1.25      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   1.25   ) =    0.105649774 [ANSWER]