Question

A very bright student is described as having an IQ that is three standard deviations above the mean. If this student's IQ were reported as a z-score, it would be:

1) 0
2) 1
3) 2
4) 3

Answer 1

The z-score that corresponds to an IQ score that is three standard deviations above the mean is 3. This score indicates a superior level of intelligence on standardized IQ tests.

Step-by-step explanation:

The z-score is a measure that describes a value's relationship to the mean of a group of values. If a student's IQ is three standard deviations above the mean, and considering that on most IQ tests the average score is 100 and one standard deviation is 15 points, their z-score would be 3. This relationship is represented as Z ~ N(0, 1), meaning a standard normal distribution where the mean (μ) is 0 and the standard deviation (σ) is 1.

A z-score of 3 indicates that the student's IQ score is three standard deviations greater than the mean. In context, most people have an IQ score within one standard deviation of the mean (between 85 and 115), while a z-score of 3 is representative of a superior intelligence level, typically above 130 on standardized IQ tests.

In summary, the z-score that corresponds to an IQ score three standard deviations above the mean is 3.