Suppose that 9 samples are taken from a normally distributed

Suppose that 9 samples are taken from a normally distributed population with an unspecified mean mu and a standard deviation of a = 3. Without knowing the results of the sampling, calculate Pr(X > 6.5|mu = 6).

Solution

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    6.5      
u = mean =    6      
n = sample size =    9      
s = standard deviation =    3      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    0.5      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   0.5   ) =    0.308537539 [ANSWER]