Question

Scores on the Wechsler intelligence quotient (IQ) test are normally distributed with a mean score of 100 and a standard deviation of 15 points. The US military has minimum enlistment standards at about an IQ score of 85. There have been two experiments with lowering this to 80 but in both cases these recruits could not master soldiering well enough to justify the costs. Based on IQ scores only, what percentage of the population does not meet US military enlistment standards?

Answer 1

15.87% of the population does not meet the minimum standards.

We use z-scores to find this probability:

z=(X-μ)/σ = (85-100)/15 = -15/15 = -1

Using a z-table (http://www.-table.com) we see that the area to the left of, less than, this is 0.1587.  This is 15.87%.