The combined math and verbal scores for students taking a national standardized examination for college admission, is normally distributed with a mean of 880 and a standard deviation of 180. If a college requires a student to be in the top 40 % of students taking this test, what is the minimum score that such a student can obtain and still qualify for admission at the college?
Percentiles should be recorded in percentage form to three decimal places.
Note that this problem does not use the rough values of the 68-95-99.7 rule (that is, the empirical rule); instead you must use more precise Z-table values for percentiles.
Exam score Z-score Percentile
50 -2
82 2
74 1
67.6 15.87