MaithiliGokarn wrote:
The arithmetic mean and standard deviation of a certain normal distribution are 13.5 and 1.5, respectively. What value is exactly 2 standard deviations less than the mean?
A. 10.5
B. 11
C. 11.5
D. 12
E. 12.5
------ASIDE---------------------------
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.
------ONTO THE QUESTION!!!-----------------------------------
The arithmetic mean and standard deviation of a certain normal distribution are 13.5 and 1.5, respectively. What value is exactly 2 standard deviations less than the mean? 2 standard deviations BELOW the mean =
13.5 - (
2)(
1.5)
= 13.5 - 3
= 10.5
= A
Cheers,
Brent
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