The weekly mean income of a group of carpenters is 1000 and

The weekly mean income of a group of carpenters is $1,000 and the standard deviation of this group is $100. The distribution is normal. What percent of the carpenters have an income of $925 or less?

Solution

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    925      
u = mean =    1000      
          
s = standard deviation =    100      
          
Thus,          
          
z = (x - u) / s =    -0.75      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -0.75   ) =    0.226627352 or 22.66% [ANSWER]