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Exam scores are normal with mean 63 and standard deviation 5. The 90th percentile has a z-score of about 1.28. What score is that?
AAbout 56.6 points
BAbout 69.4 points
CAbout 64.3 points
DAbout 76.4 points
Answer & Solution
Correct answer: B. About 69.4 points
1. The percentile value equals the mean plus the z-score times the standard deviation.
2. The mean is 63 points and the standard deviation is 5 points.
3. Multiply the z-score by the standard deviation: 1.28 times 5 is 6.4 points.
4. Add that to the mean: 63 plus 6.4 gives 69.4 points.
5. So 90 percent of the scores fall at or below 69.4 points.
6. Answering 56.6 points subtracts the 6.4 and would describe the 10th percentile.
7. Answering 64.3 points adds the z-score itself rather than the z-score times the spread.
8. Answering 76.4 points multiplies by the mean rather than by the standard deviation.
_Source: OpenStax High School Statistics (CC BY 4.0), Ch 6 "The Normal Distribution", section 6.2 Using the Normal Distribution_
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