Pecan trees are normally distributed with a mean of 10 feet

Pecan trees are normally distributed with a mean of 10 feet and a standard deviation of 2 feet. What is the probability that a randomly selected pecan tree is between 9 and 12 feet tall?

Solution

We first get the z score for the two values. As z = (x - u) sqrt(n) / s, then as          
x1 = lower bound =    9      
x2 = upper bound =    12      
u = mean =    10      
n = sample size =    1   [only 1 pecan tree]  
s = standard deviation =    2      
          
Thus, the two z scores are          
          
z1 = lower z score =    -0.5      
z2 = upper z score =    1      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.308537539      
P(z < z2) =    0.841344746      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.532807207   [ANSWER]