Final answer:
The correct answer is d) Approximately 99%.
Esther's IQ score of 146 places her well above the average, and less than 0.3% of the population would score higher. Hence, approximately 99% of the population matched her score or performed worse.
Step-by-step explanation:
To determine what percentage of the population matched her score or performed better than Esther's score of 146 on an IQ test, we need to refer to the standard distribution of IQ scores. Typically, IQ scores are assumed to follow a normal distribution with a mean of 100 and a standard deviation of 15. Esther's score of 146 is significantly above the average, placing her well within the upper extremes of the distribution.
Without the exact percentile, we can infer from the nature of the normal distribution and the standard deviations above the mean that Esther's score is beyond three standard deviations above the mean. Considering that approximately 99.7% of the population scores within three standard deviations from the mean in a normal distribution, less than 0.3% of the population would score higher than Esther. Therefore, the correct answer is d) Approximately 99%, indicating that about 99% of the population matched her score or performed worse.