The Stanford Binet Intelligence Quotient is a normed intelligence test, and its IQ measures are quite normally distributed. Its standard deviation is 16. If the test were perfectly normal in its distribution, this would mean which of the following?

Question

Quizplus · Accepted Answer

A normal distribution is symmetric around its mean, which for IQ scores is set at 100. This symmetry implies that the most common score is at the mean (A), for every score above the mean there's a corresponding score the same distance below the mean (B), and specific percentages of the population fall within certain standard deviations from the mean (C, E). The 68-95-99.7 rule for normal distributions states that about 95% of observations fall within two standard deviations (±32 points from 100), which supports (C), and about 68% fall within one standard deviation (±16 points), leaving about 14% between one and two standard deviations above the mean (E). The symmetry also means that excluding the exact mean, the population is split evenly above and below it (F). Option (D) is incorrect because individual IQ scores changing over time does not imply a zero-sum scenario where an increase in one person's score necessitates a decrease in another's; IQ scores are not conserved quantities.

The Stanford Binet Intelligence Quotient Is a Normed Intelligence Test