Final answer:
To find the percentage of the population with an IQ score between 84 and 116, calculate the z-scores for both values and find the area under the standard normal distribution curve between those z-scores. The percentage is approximately 68.27%.
Step-by-step explanation:
To find the percentage of the population with an IQ score between 84 and 116, we need to calculate the z-scores for both values and then find the area under the standard normal distribution curve between those z-scores. The formula for calculating a z-score is z = (x - mean) / standard deviation, where x is the IQ score, mean is the mean IQ score, and standard deviation is the standard deviation of IQ scores.
For an IQ score of 84, the z-score is (84 - 100) / 16 = -1. For an IQ score of 116, the z-score is (116 - 100) / 16 = 1.
The area between these z-scores represents the percentage of the population with an IQ score between 84 and 116. Using a standard normal distribution table or calculator, we find that the area is approximately 0.6827. Multiplying by 100, we get 68.27%.