If the heights of NBA players are normally distributed with

If the heights of NBA players are normally distributed with mean height of 73.5 inches and standard deviation of 2.2 inches, what is the probability of randomly selecting an NBA player that is between 72 and 73 inches tall?

Solution

We first get the z score for the two values. As z = (x - u) / s, then as          
x1 = lower bound =    72      
x2 = upper bound =    73      
u = mean =    73.5      
          
s = standard deviation =    2.2      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u)/s =    -0.681818182      
z2 = upper z score = (x2 - u) / s =    -0.227272727      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.247676963      
P(z < z2) =    0.410105839      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.162428876   [ANSWER]