Step 1 :Calculate the z-score using the formula \(Z = \frac{X - \mu}{\sigma}\)
Step 2 :Substitute the given values into the formula to get \(Z = \frac{1240 - 1538}{298} = -1\)
Step 3 :The z-score of -1 means that a score of 1240 is one standard deviation below the mean
Step 4 :Look up a z-score of -1 in the z-table to find the percentage of students who score below this
Step 5 :Approximately 15.9% of students from this school earn scores that fail to satisfy the admission requirement
Step 6 :\(\boxed{15.9\%}\) is the final answer