48. Given that intelligence quotient (IQ) scores are normally distributed with a mean of 100 and a standard deviation of 15, which of the following statements is accurate?
Answer: D
Approximately 50 percent of all IQ scores would be expected to fall above 85.
The statement accurately reflects the properties of the normal distribution of IQ scores, where a score of 85 is one standard deviation below the mean of 100. This means that approximately 50 percent of the population will score above 85.
A) The highest IQ score possible is 145.
This statement is incorrect as IQ scores are not capped at a specific number. While 145 is considered a high score and lies within the range of typical IQ assessments, there is no defined maximum IQ score in the normal distribution.
B) IQ scores of 70 and 130 are equally likely to occur.
This statement is misleading because, in a normal distribution, scores that are further from the mean are less likely to occur. Since 70 is significantly below the mean of 100 and 130 is above it, they do not have the same probability of occurrence.
C) The average IQ score in the population is 115.
This statement is incorrect. The average or mean IQ score in the population is defined as 100, not 115. A score of 115 would be one standard deviation above the mean.
D) Approximately 50 percent of all IQ scores would be expected to fall above 85.
This statement is correct. Since 85 is one standard deviation below the mean of 100, the empirical rule indicates that about 68% of the data falls within one standard deviation (between 85 and 115), which implies that around 50% of scores are above 85.
E) The likelihood of obtaining an IQ score of 115 is greater than that of obtaining an IQ score of 85.
This statement is incorrect because 85 is one standard deviation below the mean, while 115 is one standard deviation above it. The likelihood of obtaining a score of 85 is statistically higher than that of obtaining a score of 115.
Conclusion
The correct answer, D, is supported by the properties of the normal distribution, where approximately half of the scores lie above the mean minus one standard deviation. All other options either misrepresent the distribution of IQ scores or incorrectly state statistical facts about the population's IQ distribution.