assume the random variable x is normally distributed with me

assume the random variable x is normally distributed with mean= 50 and standard deviation=7. Compute the probability. p(x>39)=

Solution

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    39      
u = mean =    50      
          
s = standard deviation =    7      
          
Thus,          
          
z = (x - u) / s =    -1.571428571      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   -1.571428571   ) =    0.941958433 [ANSWER]