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About 95 percent of a normal distribution lies within two standard deviations of the mean and about 99.7 percent within three. About what percent lies between the second and third standard deviations, counting both sides?
AAbout 2 percent
BAbout 14 percent
CAbout 27 percent
DAbout 4 percent
Answer & Solution
Correct answer: D. About 4 percent
1. The band out to three standard deviations holds about 99.7 percent of the values.
2. The band out to two standard deviations holds about 95 percent.
3. The strip between them is what is left after removing the inner band.
4. Subtracting gives 99.7 minus 95.
5. That difference is about 4.7, which rounds to about 4 percent for a quick reading.
6. This total already counts both sides of the mean, so there is nothing left to double.
7. The answer of about 2 percent covers only one side of the curve.
8. The answer of about 27 percent belongs to the strip between the first and second standard deviations.
_Source: OpenStax High School Statistics (CC BY 4.0), section 6.1 The Standard Normal Distribution_
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