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Anita's grade average is 0.70 standard deviations above her college's average. Which conclusion does that figure NOT support?
AShe stands in the 70th percentile
BShe is above her college average
CHer score has a positive z-score
DShe is within one standard deviation
Answer & Solution
Correct answer: A. She stands in the 70th percentile
1. Being 0.70 standard deviations above the average gives Anita a z-score of 0.70.
2. A positive z-score means the value lies above the mean, so that reading holds.
3. Sitting above her college average follows from the same positive sign, so that reading holds too.
4. Since 0.70 is less than 1, she lies inside one standard deviation of the mean, so that reading holds.
5. A percentile is a share of people who fall at or below a score.
6. A z-score is a distance measured in standard deviations, which is a different scale entirely.
7. The number 0.70 in one scale does not become 70 percent in the other.
8. So the percentile claim is the one the figure does not support.
_Source: OpenStax High School Statistics (CC BY 4.0), section 6.1 The Standard Normal Distribution_
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