Bunuel wrote:
A set has an average (arithmetic mean) of 42 and a standard deviation of 1.8. Which of the following values is two standard deviations away from the mean?
A. 36
B. 38.4
C. 40.2
D. 43.8
E. 75.6
A little extra background on
standard deviations above and below the mean If, for example, a set has a standard deviation of
4, then:
1 standard deviation = 4
2 standard deviations = 8
3 standard deviations = 12
1.5 standard deviations = 6
0.25 standard deviations = 1
etc
So, if the mean of a set is 9, and the standard deviation is 4, then:
2 standard deviations ABOVE the mean =
17 [since 9 + 2(4) = 17] 1.5 standard deviations BELOW the mean =
3 [since 9 - 1.5(4) = 3] 3 standard deviations ABOVE the mean =
21 [since 9 + 3(4) = 21] etc.
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For this question, if the standard deviation is 1.8, then
two standard deviations = (2)(1.8) =
3.6So, two standard deviations BELOW the mean = 42 -
3.6 =
38.4And two standard deviations ABOVE the mean = 42 +
3.6 =
45.6This means there are
two correct answers.
Now check the answer choices for one of the two possible answers.
Answer:
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