Data Sufficiency

lmcelduff wrote:Hello, I was working through a GMAT Math CAT and could not solve this 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.

Help would be greatly appreciated!!

lmcelduff wrote:Hello, I was working through a GMAT Math CAT and could not solve this 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.

Help would be greatly appreciated!!

btgyes wrote:Guys...

Acc to me ans is C

and score below which failures have to take retest is 67

BarryLi wrote:Is anyone else surprised to see knowledge of the normal distribution as a requirement for being able to answer this question?

btgyes wrote:Guys...

C is fine...

Can Experts plz confirm the ans... acc to me it should be 72-5=67

stormier wrote:

lmcelduff wrote:Hello, I was working through a GMAT Math CAT and could not solve this 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.

Help would be greatly appreciated!!

A normal distribution is a bell-shaped curve, symmetrical about its mean. You can read more about it here:

https://mathworld.wolfram.com/NormalDistribution.html

So imagine a frequency distribution plot, showing frequency (count of students) on the y-axis and score on the x-axis. The question stimulus asks the score at or blow which the recruits will have to retest. In other words, its asking the point on the x-axis to the left of which 16 % of students lie.

To be able to answer this, the distribution curve must be known completely. i.e. you should not only know the height of the curve, but also the width of the curve (typically characterized by FWHM - Full Width at Half Maximum)

Mean = 72 => the bell curve is symmetrical about x=72.

1. There are a total of 500 students.


From this information alone you cannot "fix" the curve. For example, you could have 400 students at score of 72, and 50 each at score of 70 and 74. In such a case the bell would be very narrow and sharp looking - high at the mean and narrow width.

You could also have a broad-looking curve -> 200 at 72, 100 each at 60 and 84, and 50 each at 50 and 94.

In other words, statement 1 says that area under the curve is 500, but does not give any information on the width or height of the curve. The curve can be drawn in several ways, hence INSUFFICIENT.

2. 10 recruits scored 82 or higher.

From this information alone, a fixed curve cannot be drawn. Since the total number of students is not known, one could a curve such that 10 have 82 or higher score, any number of students at the mean value of 72. It could be a 100 or 1000. i.e. with this information, the height of the curve cannot be fixed. Hence INSUFFICIENT.

Combine the two ->

Now, parameters required to fix the curve are known.

Area under the curve = 500. The mean = 72. A point on the right of the mean through which the curve passes. (1) and (2) combined are sufficient to fix the curve and hence answer the question.

Answer C.

However, this question is outside the GMAT scope and would never appear on the test.

lmcelduff wrote:I present this question to sanju09 (the website-cited GMAT expert):
for all future problems on the GMAT where standard deviation is involved, and they use the term normally distributed, am I always going to use the 34%, 14%, 2% bell curve to represent 1st, 2nd, and 3rd SD? The reason I ask is because in prior statistics classes, I have also seen normalized standard deviation to be defined as 1σ* = 68%, 2σ = 95%, 3σ = 99%. Could you please confirm/deny my posit to your inquiry, as I wanted to be certain as to the accuracy of this approach?

Furthermore, according to the response received from user stormier, the question I presented is outside the scope of the current GMAT and therefore irrelevant altogether. Could you also provide brief commentary on whether or not this is true?

to user BarryLi: I also was confused as to why this question would be on the GMAT, as all the literature I have read thus far about this test states that only basic knowledge need be applied to take this exam. It seems you would need to know a little bit about statistics/SD curve to answer this question.

Thanks!


*σ = SD

lmcelduff wrote:I present this question to sanju09 (the website-cited GMAT expert):
for all future problems on the GMAT where standard deviation is involved, and they use the term normally distributed, am I always going to use the 34%, 14%, 2% bell curve to represent 1st, 2nd, and 3rd SD? The reason I ask is because in prior statistics classes, I have also seen normalized standard deviation to be defined as 1σ* = 68%, 2σ = 95%, 3σ = 99%. Could you please confirm/deny my posit to your inquiry, as I wanted to be certain as to the accuracy of this approach?

Furthermore, according to the response received from user stormier, the question I presented is outside the scope of the current GMAT and therefore irrelevant altogether. Could you also provide brief commentary on whether or not this is true?

to user BarryLi: I also was confused as to why this question would be on the GMAT, as all the literature I have read thus far about this test states that only basic knowledge need be applied to take this exam. It seems you would need to know a little bit about statistics/SD curve to answer this question.

Thanks!


*σ = SD