Final answer:
Using the 68-95-99.7 rule, the exact percentage of people with IQ scores between 52 and 68 cannot be determined. Approximately 2.35% of the population will have an IQ between these values, but the rule doesn't provide the precise percentage for this specific range.
Step-by-step explanation:
The question asks which percentage of people should have IQ scores between 52 and 68. This question is related to the properties of the normal distribution and the 68-95-99.7 rule, also known as the empirical rule. This rule states that in a normal distribution, about 68% of the values fall within one standard deviation from the mean, 95% within two standard deviations, and 99.7% within three standard deviations. An average IQ score is 100, with a standard deviation of 15. Therefore, a score of 52 is more than three standard deviations below the mean, and a score of 68 is just over two standard deviations below the mean. According to the empirical rule, 2.5% of scores would fall more than two standard deviations below the mean and 0.15% more than three standard deviations below the mean, by summing these (and considering both tails of the distribution), we would get approximately 2.5% + 2.5% + 0.15% + 0.15% = 5.3% of people beyond two standard deviations from the mean. Since 95% of people are within two standard deviations (both above and below), we subtract the 5.3% (who are beyond) from 100% to get 94.7%. Therefore, we know that 2.35% will be between two and three standard deviations below, and we subtract half the percentage of the population within one standard deviation from the mean (34%) from the lower part. Thus, we can estimate that around 2.35% of person should have an IQ between 52 and 68. However, the exact percentage of people within this specific range of IQ scores is not exactly given by the 68-95-99.7 rule and thus the answer would be Cannot be determined based on this rule alone.