Final answer:
The student's SAT score of 1100 is 0.354 standard deviations above the mean, which is above average but still within the average range as it is less than one standard deviation from the mean.
Step-by-step explanation:
To evaluate how well a student scored on the SAT compared to the average test taker, it is essential to calculate the z-score. A z-score represents how many standard deviations an element is from the mean. For the student who scored an 1100 on the SAT:
- Z = (X - Mean) / Standard Deviation
- Z = (1100 - 1026) / 209
- Z = 74 / 209
- Z ≈ 0.354
This z-score indicates that the student scored approximately 0.354 standard deviations above the mean SAT score. Considering that the mean SAT score is 1026 with a standard deviation of 209, the student's score of 1100 is above average but not exceptionally high above it. In the context of a normal distribution, we often refer to scores within one standard deviation above or below the mean as average, which implies that this student's score would still be considered within the average range of performance.
Referring to example 67 and example b:
- a 720 SAT math score corresponds to a z-score of 1.74, (720-520)/115, which means it is 1.74 standard deviations above the mean.
- In example b, 692.5 is 1.5 standard deviations above the mean SAT math score.
Thus, although the student with an 1100 SAT score did well compared to the average test taker, the score is within one standard deviation of the mean and is not among the highest scores, such as those exceeding 1.5 standard deviations above the mean.