The lifetimes of all the batteries produced by a certain

[Guest]

Could an instructor/someone please explain this one?
The problem is attached and the answer is D.

How do you attack a problem like this? What's the underlying concept that can/will show up again in a different form on the actual test?

Thanks.

[GMAT 2007]

[editor: this post was corrected on 23/jul/2008 -- there were some faulty numbers in it]

The problem deals with the Standard deviation in the distribution. By definition we know the standard deviation is the measure of how spread out the distribution is. Also it is given the distribution is symmetric about the mean m. It means the elements are evenly disributed around the mean.

[editor: actually, you don't need to know anything at all about the meaning of standard deviation to solve this problem; the symmetry of the distribution is the only salient fact. see my post below, dated 23/jul/08. --ron]

For ex - in distribution 2,4,6,8,10 - elements (2,4) & (8,10)are symmetric about the mean 6.

Now, we need to find the percent of the distribution greater then (m+d)

Statement (1) -

68% of the distribution lies between (m-d) & (m+d). Since the distribution is symmetric, Hence

The percentage distribution between (m-d) & m = 34%
The percentage distribution between m & (m+d) = 34%

Also,
The percentage distribution less than (m-d) will be 16% and
The percentage distribution greater than (m+d) will be 16%, Sufficient.

Statement (2) -

The percentage distribution less than (m-d) = 16%. From the question we know the distribution is symmetric, so 50% of the distribution should be less than m and 50% of the distribution should be greater than m.

Since, the percentage distribution less than (m-d) = 16%
So the percentage distribution between (m-d) & m = 34%
and the percentage distribution between m & (m+d) will be 34% too and
Percentage distribution greater than (m+d) will be 16%

It is sufficient too.

GMAT 2007

[Anadi]

Symmetric distribution does not mean that mean is evenly distributed. It's just symmetric or equally distributed on both the sides of the mean. (may be one of the tutors can explain more).

[guest]

32, and 32 add up to 64, not 68 - as is stated in statement 1 . what am i missing?

[Guest]

Instructors - any thought on this?

[Guest]

It looks like a typo. I think 32 should be changed to 34 in the explanation.

[ack]

Definitely a typo - It should be 34 + 34 = 68
The area under the curve for both m+d and m-d is 34

[Guest]

Instructors- any thoughts on the approach by GMAT 2007?

[Guest]

bump

[RonPurewal]

Instructors- any thoughts on the approach by GMAT 2007?

his/her approach is correct. the only caveat is that every single '32' in that explanation should be changed to '34' (and there are quite a few of them to change).

--

the most important thing i want to point out about this problem is that the concept of the standard deviation is completely irrelevant to the problem's solution; all that matters is that the battery lives are symmetrically distributed. all of the reasoning required to solve the problem would work just as correctly, and in precisely the same way, if 'd' were taken to stand for some random number rather than the standard deviation.

(try it yourself; just delete the entire mention of standard deviation from the original problem statement, and note that the solution still works.)