Scores on the sat verbal test in recent years follow approximately the n(504,111) distribution. the proportion of students scoring under 400 is?

If you know how to use built-in statistical functions on a calculator such as the TI-83 or 84, you can solve this problem with one press of the ENTER key on the calculator:

normalcdf(-100, 400, 504,  111) = 0.17 (answer)

Otherwise, find the z-score associated with 400:

       400-504
z= , and the use a z-score table to find the area under the 
          111          standard normal curve to the left of this z value.