Answer :
Final answer:
The 10-year-old's score of 140 on the IQ test is a lot greater than the mean (100). By calculating the Z-score, we find out that the child's score is 2.67 standard deviations above the mean, indicating a score in the top 1%, and therefore in the gifted and talented range.
Explanation:
In this scenario, the 10-year-old child has scored 140 on an IQ test, which is considerably higher than the average score of 100. The standard deviation of 15 measures the variability of scores, but to determine where this particular score stands, we need to use the concept of Z-scores.
The Z-score represents how many standard deviations the particular score or value is from the mean. In this case, 140-100 = 40, so the child's score is 40 points higher than the mean. We then divide these 40 points by the standard deviation of 15, resulting in a Z-score of approximately 2.67. This means that the child's score is 2.67 standard deviations above the mean score. In the context of IQ scores and normal distribution, scoring 2.67 standard deviations above the mean places this child in the top 1% of the population, therefore, the statement 'This child scores in the gifted and talented range' would be correct.
Learn more about Z-score here:
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