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
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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) = 3.6
So, two standard deviations BELOW the mean = 42 - 3.6 = 38.4
And two standard deviations ABOVE the mean = 42 + 3.6 = 45.6
This means there are two correct answers.
Now check the answer choices for one of the two possible answers.

Answer:
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Two standard deviations above the mean is 42 + 2 x 1.8 = 42 + 3.6 = 45.6.

Two standard deviations below the mean is 42 - 2 x 1.8 = 42 - 3.6 = 38.4.

Answer: B
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