Final answer:
The percent of all people who fall within 15 points of the average IQ score of 100, achieving scores between 85 and 115, is 68%.
Therefore, option c. 68% is the correct answer
Step-by-step explanation:
The question is asking about the distribution of IQ scores around the mean of 100. According to the principles of a normal distribution, which applies to IQ scores, we can determine that 68% of the population falls within one standard deviation of the mean. In the context of IQ scores, one standard deviation is 15 points.
Therefore, if the average score is 100, then scores between 85 and 115 (100 minus 15 and 100 plus 15) would include 68% of the population. This is under the assumption that the IQ scores are normally distributed.
To find the percent of all people who fall within 15 points of the average score, we need to find the area under the normal distribution curve between 85 and 115. The average score is 100 and the standard deviation is 15 (1 standard deviation is 15 points).
We can use the Z-score formula to calculate the area under the curve. The Z-score for the lower limit is (85-100)/15 = -1, and the Z-score for the upper limit is (115-100)/15 = 1.
The area between -1 and 1 standard deviation is approximately 68%. Therefore, option c. 68% is the correct answer