Assume that all of your job applicants must take a test, and that the scores on this test are normally distributed.

The “selection ratio” is the cutoff point you use in your hiring process. For example, a selection ratio of 20%

means that you will accept applicants for jobs who rank in the top 20% of all applicants. If you choose a selection ratio of 20%, the average test score of those selected will be 1.40 standard deviations above average of all applicants. Use simulation to verify this fact, proceeding as follows.

a. Show that if you want to accept only the top 20%

of all applicants, you should accept applicants whose test scores are at least 0.842 standard deviation above average. (No simulation is required here. Just use the appropriate Excel normal function.)

b. Now generate 1000 test scores from a normal distribution with mean 0 and standard deviation