The scale of scores on the Wechsler Adult Intelligence Scale (WAIS) is set separately for each age group and is approximately normal with mean 100 and standard deviation 15. Use this distribution and the 68-95-99.7 rule, (68% of observations fall within (1) (standard deviation of the mean), 95% of the observations fall within (2) (standard deviations) of the mean, 99.7% of observations fall within (3) (standard deviations) of the mean) to answer the following problem: People with WAIS scores below 70 are considered mentally retarded, when for example, applying for disability benefits. What percent of adults are retarded by this criterion?
Solution: We need to compute
which means that 2.275% of adults are retarded by this criterion.