Final Answer:
Approximately 84% of the population has an IQ score greater than 114.
Step-by-step explanation:
IQ scores are standardized to have a mean of 100 and a standard deviation of 15. This means that the majority of the population falls within one standard deviation of the mean.
To find the percentage of people with an IQ score greater than 114, we need to look at the area under the normal distribution curve to the right of 114. Using the Z-score formula, where Z = (X - μ) / σ (where X is the IQ score, μ is the mean, and σ is the standard deviation), we find that the Z-score for an IQ of 114 is (114 - 100) / 15 = 0.9333.
Consulting a standard normal distribution table or calculator, we find that the percentage of the population with a Z-score greater than 0.9333 is approximately 0.1788.
Subtracting this from 1 gives us the percentage of people with an IQ greater than 114, which is approximately 0.8212. Multiplying this by 100, we find that around 82.12% of the population has an IQ greater than 114.
In summary, the final answer is that approximately 84% of the population has an IQ score greater than 114. This is derived by considering the standard normal distribution and using the Z-score to determine the percentage of the population above a given IQ threshold.
The calculation takes into account the mean and standard deviation of IQ scores, providing a statistically sound basis for understanding the distribution of intelligence in the population.