Data Sufficiency

Dear all, when I practice for GMat in Cracking the Gmat 2009 edition by Princeton. I met a question. It was so hard that i couldn't understand it even I read it explanation. Here is the problem...

The members of the newest recruiting class of a certain military organization are taking their physical conditioning test and those who score in the bottom 16 percent will have to retest. If the scores are normally distributed and have an arithmetic mean of 72, what is the score at or below which the recruits will have to retest?

(1) there are 500 recruits in the class

(2) 10 recruits scored 82 or higher

Note: this is Data Sufficiency Question.

bupbebeo wrote:Dear all, when I practice for GMat in Cracking the Gmat 2009 edition by Princeton. I met a question. It was so hard that i couldn't understand it even I read it explanation. Here is the problem...

The members of the newest recruiting class of a certain military organization are taking their physical conditioning test and those who score in the bottom 16 percent will have to retest. If the scores are normally distributed and have an arithmetic mean of 72, what is the score at or below which the recruits will have to retest?

(1) there are 500 recruits in the class

(2) 10 recruits scored 82 or higher

Note: this is Data Sufficiency Question.

This is a Standard Deviation question .

Mean = 72

In a bell curve for SD 34% , 14 % and 2 % will correspond to the 1 st , 2 nd and 3 rd SD on each side of the mean .

Now we are given bottom 16% will have to retest that means people whit marks that are 1 SD less than the mean .

So we need to calculate the SD in order to find the score .


Statement (1) there are 500 recruits in the class

dose not say any thing about SD . Not sufficient .


Statement (2)10 recruits scored 82 or higher

We can not deduce if 10 recruit represent 2% or 14% of the population .

So we can not say what the SD is .

Not sufficient .

Combine (1) and (2)

Total recruits = 500 .

10 represents 2% of the population .

Therefore score of 82 represents 3 SD to the right of mean .

82-72(mean) = 10 .

Now 82 is 3 SD from mean hence SD = 10 / 3 = 3.33

Now we can calculate the score below which the recruits will have to retest .

This score will be 2 SD to the left of mean .

That is 72 - 2(3.33) = 65.4

[spoiler]
So answer is C .[/spoiler]

IMO C

In a bell curve for SD 34% , 14 % and 2 % will correspond to the 1 st , 2 nd and 3 rd SD on each side of the mean .


How do you know this? If it is some statistical property, can you tell me where to study these kinds of properties or so from?

Thanks

eaakbari wrote:In a bell curve for SD 34% , 14 % and 2 % will correspond to the 1 st , 2 nd and 3 rd SD on each side of the mean .


How do you know this? If it is some statistical property, can you tell me where to study these kinds of properties or so from?

Thanks

This is what you can learn from Std 8 th or 9 th maths books. Go through the basic understanding of standard deviation.

When in school you must have plotted the frequency curve , I know most of us dont remember including me heheheheheeee.


Have a look : https://en.wikipedia.org/wiki/Standard_deviation

https://www.robertniles.com/stats/stdev.shtml


But you dont need to remember all this stuff . All you need to know what is Mean , Median , Standard Deviation , and also look at OG 12page 115 .

Hope this helps .

Thanks that was hugely helpful

bupbebeo wrote:Dear all, when I practice for GMat in Cracking the Gmat 2009 edition by Princeton. I met a question. It was so hard that i couldn't understand it even I read it explanation. Here is the problem...

The members of the newest recruiting class of a certain military organization are taking their physical conditioning test and those who score in the bottom 16 percent will have to retest. If the scores are normally distributed and have an arithmetic mean of 72, what is the score at or below which the recruits will have to retest?

(1) there are 500 recruits in the class

(2) 10 recruits scored 82 or higher

Note: this is Data Sufficiency Question.

Thanks for the note, very useful!

Yes, it is a hard question that very a few lucky test writers find on GMAT. Standard Deviation is a basic concept, but the Bell-Curve is not so basic to be comprehended generally. We can answer this in a flash of moment if the Normal Distribution doesn't make us abnormal. Such a plane and simple question, stem is missing both of the information, so [spoiler]C[/spoiler].

well done rockeyb! good to see that you haven't suggested to learn all that your sent link(s) contain, because no guidance is far better than misguidance, you rock rockeyb!!

sanju ,

Thanks mate , I am just trying to give back what I got from this forum in fact I have learned a lot from this forum form post by people like you , gmatmachoman , febonaci , harsha , thefeonix and others too .

So if I can help at least a single person I am doing my little bit .

Thanks again mate .

Cheers !!!!

rockeyb wrote:

bupbebeo wrote:Dear all, when I practice for GMat in Cracking the Gmat 2009 edition by Princeton. I met a question. It was so hard that i couldn't understand it even I read it explanation. Here is the problem...

The members of the newest recruiting class of a certain military organization are taking their physical conditioning test and those who score in the bottom 16 percent will have to retest. If the scores are normally distributed and have an arithmetic mean of 72, what is the score at or below which the recruits will have to retest?

(1) there are 500 recruits in the class

(2) 10 recruits scored 82 or higher

Note: this is Data Sufficiency Question.

This is a Standard Deviation question .

Mean = 72

In a bell curve for SD 34% , 14 % and 2 % will correspond to the 1 st , 2 nd and 3 rd SD on each side of the mean .

Now we are given bottom 16% will have to retest that means people whit marks that are 1 SD less than the mean .

So we need to calculate the SD in order to find the score .


Statement (1) there are 500 recruits in the class

dose not say any thing about SD . Not sufficient .


Statement (2)10 recruits scored 82 or higher

We can not deduce if 10 recruit represent 2% or 14% of the population .

So we can not say what the SD is .

Not sufficient .

Combine (1) and (2)

Total recruits = 500 .

10 represents 2% of the population .

Therefore score of 82 represents 3 SD to the right of mean .

82-72(mean) = 10 .

Now 82 is 3 SD from mean hence SD = 10 / 3 = 3.33

Now we can calculate the score below which the recruits will have to retest .

This score will be 2 SD to the left of mean .

That is 72 - 2(3.33) = 65.4

[spoiler]
So answer is C .[/spoiler]

Ans is C.. That very fine....

BUT

acc to me, 82 is 2 S.D from mean not 3 S.D because it is saying that 10 recruit scored 82 or higher

that means there may be people who scored more than 82

that means those 2 % start from 2nd S.D and end at 3rd S.D

#now if you take 82 3 S.D from mean ie 72 then where you will occupy a person who scored let say 90 ?????#

so 10 = 2 S.D

=> S.D = 5

AND ans will be 72-5 = 67

It would be great if any expert could comment on this....

thanks

---- sorry for raising this thread, but the one was referenced by sanju recently in SD problem as a good discussion
@rockeyb: first of 10 recruits tested with the score 82 or higher makes as you correctly mentioned below 2% and please don't forget the 68-95-99.7% rule (here as a reminder to our business stats class https://www-stat.stanford.edu/~naras/jsm ... nsity.html )... so we cannot make it 3 standard deviations by taking 82-72 -- there are data distributed above 98% up to 99.7%

and all the solution proposed below falls into wrong SD calculation, but an overall approach was interesting

rockeyb wrote:

bupbebeo wrote:Dear all, when I practice for GMat in Cracking the Gmat 2009 edition by Princeton. I met a question. It was so hard that i couldn't understand it even I read it explanation. Here is the problem...

The members of the newest recruiting class of a certain military organization are taking their physical conditioning test and those who score in the bottom 16 percent will have to retest. If the scores are normally distributed and have an arithmetic mean of 72, what is the score at or below which the recruits will have to retest?

(1) there are 500 recruits in the class

(2) 10 recruits scored 82 or higher

Note: this is Data Sufficiency Question.

This is a Standard Deviation question .

Mean = 72

In a bell curve for SD 34% , 14 % and 2 % will correspond to the 1 st , 2 nd and 3 rd SD on each side of the mean .

Now we are given bottom 16% will have to retest that means people whit marks that are 1 SD less than the mean .

So we need to calculate the SD in order to find the score .


Statement (1) there are 500 recruits in the class

dose not say any thing about SD . Not sufficient .


Statement (2)10 recruits scored 82 or higher

We can not deduce if 10 recruit represent 2% or 14% of the population .

So we can not say what the SD is .

Not sufficient .

Combine (1) and (2)

Total recruits = 500 .

10 represents 2% of the population .

Therefore score of 82 represents 3 SD to the right of mean .

82-72(mean) = 10 .

Now 82 is 3 SD from mean hence SD = 10 / 3 = 3.33

Now we can calculate the score below which the recruits will have to retest .

This score will be 2 SD to the left of mean .

That is 72 - 2(3.33) = 65.4

[spoiler]
So answer is C .[/spoiler]