SAT Math scores for the population of seniors at a large high school are approximately Normal with mean and standard deviation . A normal curve is shown with the value marked.
Normal curve (SAT Math)
|
| .-''''-.
| .-' '-.
| .' '.
| / \
|----------|----|----|----|----|----|----|----> x
320 400 480 560 640 720 800
\mu=560 <u>640</u>
Which statement about the marked value is correct?
- A score of 640 is about 1 standard deviation above the mean, so it is higher than typical but not extremely unusual. (correct answer)
- A score of 640 is about 2 standard deviations above the mean, so it is extremely unusual.
- A score of 640 is about 1 standard deviation below the mean, so it is lower than typical.
- A score of 640 is about 1 standard error above the mean, so it is higher than typical.
- A score of 640 is about 1 standard deviation above the mean, so fewer than 5% of seniors score above 640.
Explanation: This question evaluates score interpretation in normal distributions for AP Statistics. SAT scores are normal with μ = 560 and σ = 80. The z-score for 640 is (640 - 560) / 80 = 1, so 1 standard deviation above the mean. The empirical rule shows this within the 68% central range, higher but not extremely unusual. Distractor choice E claims fewer than 5% score above, but actually about 16% do beyond +1σ. In normal models, referencing μ and σ allows standardization, with the 68-95-99.7 rule helping gauge typicality and proportions.