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Assuming the normal distribution, about what proportion of a sample lies between the mean & 2 SDs above the mean?

A. 34%
B. 47%
C. 68%
D. 95%
E. None of the above

1 Answer

7 votes

Final answer:

The proportion of a sample from a normal distribution that lies between the mean and 2 standard deviations above the mean is about 47.5%, but the closest answer provided in whole numbers is 47% (Option B).

Step-by-step explanation:

According to the Empirical Rule for a normal distribution, about 68% of the data falls within one standard deviation of the mean, about 95% within two standard deviations, and over 99% within three standard deviations. For the part of the question asking

About what proportion of a sample lies between the mean & 2 SDs above the mean?

We need to remember that a normal distribution is symmetrical about the mean. Therefore, if approximately 95% of the data lies within two standard deviations (both above and below the mean), half of this percentage, or approximately 47.5%, will lie between the mean and 2 standard deviations above the mean. However, since the options are in whole numbers, the closest answer to 47.5% would be B. 47%.

User Zachary Turner
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