Probability question - interpreting equation

[infiniti007]

X Frequency
1 3
2 1
3 3
4 1
5 3
6 1
7 3

The variable x takes on integer values between 1 and 7, inclusive, as shown in the table above. What is the probability that the absolute value of the difference between the mean of the distribution, which is 4, and a randomly chosen value of x will be greater than 3/2?

A.) 8/15
B.) 4/7
C.) 4/5
D.) 6/7
E.) 8/7

My specific question on this problem is in regard to interpreting the equation specified in the question. I interpreted "the absolute value of the difference between the mean of the distribution, which is 4, and a randomly chosen value of x" to mean: |4-x|.

This question comes from the GMAT Prep question pack and the answer description uses the equation: |x-4|. I presume these are the same since I arrived at the same answer, but I'd like to know how to properly interpret "the difference between a and b" and how that translates to an equation. i.e. "a-b" or does it mean "b-a"?

Thanks

[[email protected]]

Hi infiniti007,

Since we're dealing with an Absolute Value, either the "4" or the "X" can 'come first' (so you can use |X-4| or |4-X| and the result will be the same).

Here are a couple of examples:

|1-4| = |4-1|

|5-4| = |4-5|

When a prompt asks for the difference between two values, but does NOT include an Absolute Value, then subtraction is required, but that difference could be POSITIVE or NEGATIVE (depending on which value comes first).

For example:
1-4 = -3
4-1 = +3

When this type of concept shows up in an Official GMAT question, the prompt will often refer to the "positive difference between X and Y" (which is just another way of saying the Absolute Value difference).

For example:

"What's the positive difference between 4 and 5" is the same as "what's the positive difference between 5 and 4."

If you're in doubt though, then put the first variable named in 'front':

The difference between A and B is (A-B).

Just make sure to note that B COULD be bigger than A.

GMAT assassins aren't born, they're made,
Rich

[Dabhishek]

will you pls provide solution too

[[email protected]]

HI Dabhishek,

The table consists of 15 values (three 1s, one 2, three 3s, one 4, etc.). We're asked for the probability that a randomly chosen value will be MORE than 3/2 'away' from 4.

The values that fit that description are the three 1s, the one 2, the one 6 and the three 7s. That's 8 out of 15.

Final Answer: A

GMAT assassins aren't born, they're made,
Rich