The average height of flowering cherry trees in a certain nu

The average height of flowering cherry trees in a certain nursery is 9.5 feet. If the heights are normally distributed with a standard deviation of 1.3 feet, find the probability that a tree is less than 11.5 feet tall.

Solution

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    11.5      
u = mean =    9.5      
          
s = standard deviation =    1.3      
          
Thus,          
          
z = (x - u) / s =    1.538461538      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   1.538461538   ) =    0.938032097 [ANSWER]