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About 99.7 percent of a normal distribution lies within three standard deviations of the mean. About what percent lies between the mean and three standard deviations on one side only?
AAbout 25 percent
BAbout 50 percent
CAbout 68 percent
DAbout 99 percent
Answer & Solution
Correct answer: B. About 50 percent
1. Three standard deviations either side of the mean covers about 99.7 percent of the values.
2. A normal curve is symmetric, so the two sides of the mean hold equal shares.
3. Taking one side only means taking half of that 99.7 percent.
4. Half of 99.7 is about 49.85.
5. That rounds to about 50 percent.
6. The answer of about 99 percent forgets to halve and keeps both sides.
7. The answer of about 68 percent is the two-sided share for one standard deviation, not three.
8. The answer of about 25 percent would be a quarter of the curve, which no empirical rule band gives.
_Source: OpenStax High School Statistics (CC BY 4.0), section 6.1 The Standard Normal Distribution_
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