In screening applicants for a position, testing is one device used, in addition to interviews and background investigations. Such tests often focus on mechanical aptitudes and skills, although for some positions, tests may focus on personality psychology. One such test for manual dexterity administered to a large number of applicants showed that the time required for completion was approximately normally distributed with a mean of 12 minutes and with a standard deviation of 1.5 minutes.
Based on this information, (a) what proportion of applicants finish in less than 14 minutes? (b) If only the best 25% of the applicants (using the dexterity test as the criterion of best) are to be passed through this screening stage, within what time must an applicant complete this test in order to pass?