DS : GMATprep : Lifetimes of Batteries

[hiteshdalal]

I came across one DS problem from GMATPrep download from www.mba.com

The question is :

The lifetimes of all the batteries produced by a certain company in a year have a distribution that is symmetric about the mean m. If the distribution has a standard deviation of d, what percent of the distribution is greater than m + d ?

(a) 68 percent of the distribution lies in the interval from m- d to m+d, inclusive

(b) 16 percent of the distribution is less than m - d

How is the statement (b) sufficient ?

[jnelson0612]

I came across one DS problem from GMATPrep download from http://www.mba.com

The question is :

The lifetimes of all the batteries produced by a certain company in a year have a distribution that is symmetric about the mean m. If the distribution has a standard deviation of d, what percent of the distribution is greater than m + d ?

(a) 68 percent of the distribution lies in the interval from m- d to m+d, inclusive

(b) 16 percent of the distribution is less than m - d

How is the statement (b) sufficient ?

hitesh,
The problem says that the distribution is symmetrical. This means that there are exactly the same number of data points within each standard deviation on both sides of the mean.

The mean is m and the standard deviation is d. Thus, one standard deviation from the mean contains all the points within m-d to m+d.

The question is what percentage of the distribution is greater than m+d? In other words, what percentage of the distribution is greater than one standard deviation. Well, since I have a symmetrical distribution, I know this percentage must be equal to the percentage of the distribution that is less than m-d, or less than one standard deviation. This information is provided in B; thus, I know that m+d is also equal to 16%.

Please let me know if this does not make sense.

Thank you,

[hiteshdalal]

Hi Jamie,
I got the concept, request you to elaborate on how 16% is the value..

Regards,

[jnelson0612]

Hi Jamie,
I got the concept, request you to elaborate on how 16% is the value..

Regards,

hitesh,
16% is the value because that is what answer choice B tells us: 16% of the distribution is less than m-d. We know that m-d is one standard deviation below the mean, so 16% of the distribution is below one standard deviation. Because we have a symmetrical graph, we now know that 16% of the distribution is also ABOVE one standard deviation above the mean (m+d), thus answering our question.

Thank you,

[bedisha.karmakar]

Hi Jamie,

My confusion here is , if we know that the graph is symmetrical, then the values fall in the range of 2%, 14% and 32% on both sides of the mean. here the question states that m-d and m+d = 68%, hence why cant we conclude that m+ 2d and m+3d will be 16 % ?

Please help !!! badly confused !

Rgds,
Bedisha

[RonPurewal]

please don't start new threads without searching the forum -- this problem has 3-4 threads in the forum already.

here's the most comprehensive post on this problem so far:
post32615.html#p32615