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.
In a normal distribution, the mean divides the data into two equal parts. Given that the mean IQ score is 100, approximately 50 percent of scores will fall above 85, which is one standard deviation below the mean.
A) The highest IQ score possible is 145.
This statement is incorrect because while 145 may be a high IQ score, there is no theoretical upper limit to IQ scores in a normal distribution. Scores can extend beyond 145, although they become increasingly rare.
B) IQ scores of 70 and 130 are equally likely to occur.
This statement is also incorrect. In a normal distribution, scores that are further from the mean (like 70 and 130) have different probabilities. The score of 70 is significantly below the mean, making it less likely to occur than a score of 130, which is above the mean.
C) The average IQ score in the population is 115.
This statement is incorrect as the average (mean) IQ score is actually 100, not 115. The mean is a critical value in understanding the distribution of IQ scores.
D) Approximately 50 percent of all IQ scores would be expected to fall above 85.
This statement is accurate because, in a normal distribution with a mean of 100, the score of 85 is one standard deviation below the mean. Therefore, about half of the population will score above this value.
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. Since 115 is closer to the mean than 85, while it may seem intuitive, the distribution indicates that scores further from the mean (like 85) actually encompass a larger portion of the population than scores that are closer, such as 115.
Conclusion
The correct answer is D because it accurately reflects the properties of a normal distribution where approximately half of the scores lie above one standard deviation below the mean. The other options either misrepresent statistical principles or incorrectly state values related to IQ distributions. Thus, option D stands out as the only accurate statement regarding the distribution of IQ scores.