If a certain set of GMAT test score has a mean of 550

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

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

Two standard deviations from the mean is:

550 - 2(23) = 504 and 550 + 2(23) = 596.

We see that Rob’s score can be any number from 504 to 596. So 402 cannot be Rob’s score.

Answer: A