BTGModeratorVI wrote: ↑Sun Feb 23, 2020 6:48 am
If a certain set of GMAT test score has a mean of 550 and a standard deviation of 23, and Rob's score is within two standard deviations from the mean, which of the following CANNOT be Rob's score?
A) 402
B) 543
C) 550
D) 583
E) 590
Source: Economist
Answer: A
-----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.
-----------------------------------
Mean =
550
Standard deviation =
23
So, 2 standard deviations BELOW the mean =
550 - (2)(
23) =
504
And 2 standard deviations ABOVE the mean =
550 + (2)(
23) =
596
GIVEN: Rob's score is within two standard deviations from the mean
So Rob score is BETWEEN
504 and
596
Check the answer choices.....
Answer choice A does NOT fall within this range
Answer: A
Cheers,
Brent
