GreenlightTestPrep wrote:
The scores on a given history test are normally distributed about a mean of 72 points. A score of 78 is in the nth percentile while a score of 84 is in the mth percentile.
Quantity A |
Quantity B |
n – 50 |
m – n |
A) The quantity in Column A is greater.
B) The quantity in Column B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Of a key piece of information here is that
the scores of 72, 78 and 84 are all EQUALLY SPACEDThat is, there are six points between 72 and 78, and there are six points between 78 and 84.
Important concept: In a normal distribution, the mean is approximately in the 50th percentile.So, a test score of 72 points is a 50th percentile score (since we're told the mean = 72).
We're told that 78 is in the nth percentile
So
n – 50 = the PERCENTAGE of scores between 78 and 72We're told that 84 is in the mth percentile
Likewise,
m – n = the PERCENTAGE of scores between 84 and 78We can see that the area between
78 and 72 is GREATER THAN the area between
84 and 78So, the
PERCENTAGE of scores between 78 and 72 is greater than the
PERCENTAGE of scores between 84 and 78In other words,
n - 50 >
m - nAnswer: A
IMPORTANT: Since we don't know the standard deviation of this distribution, there is no way to determine the exact values of m and n.
In other words, there's no way to determine exactly where 78 and 84 lie on the normal distribution.
That, however, doesn't change the answer to the question.
We need only recognize that 72, 78 and 84 are all EQUALLY SPACED.
So, even if the distribution looks like this...
... We can still see that the area between
78 and 72 is GREATER THAN the area between
84 and 78As such, we can still conclude that
n - 50 >
m - nAnswer: A
Cheers,
Brent
_________________
Brent Hanneson - founder of Greenlight Test Prep