if 500 fish are randomly selected how many would be shorter

if 500 fish are randomly selected how many would be shorter than 9 inches. mean is 10 stand dev is 2

Solution

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    9      
u = mean =    10      
          
s = standard deviation =    2      
          
Thus,          
          
z = (x - u) / s =    -0.5      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -0.5   ) =    0.308537539

Thus, there are 0.308537539*500 = 154.2687695 or around 154 shorter than 9 in.

[ANSWER, 154.2687695 OR AROUND 154]