The results of a test that follows a normal distribution hav

The results of a test that follows a normal distribution have a mean value of 10.0 and a standard deviation of 1. Find the probability that a single reading is between 9 and 12.

Solution

We first get the z score for the two values. As z = (x - u) / s, then as          
x1 = lower bound =    9      
x2 = upper bound =    12      
u = mean =    10      
          
s = standard deviation =    1      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u)/s =    -1      
z2 = upper z score = (x2 - u) / s =    2      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.158655254      
P(z < z2) =    0.977249868      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.818594614   [ANSWER]