Data Sufficiency problem from Princeton Review

[pranavc]

I have trouble with the question below. Any help would be much appreciated.

3. 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% 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 recruits have to retest?

(1) There are 500 recruits in the class.
(2) 10 recruits 82 or higher.

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

(C) BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient.

(D) EACH statement ALONE is sufficient.

(E) Statements (1) and (2) TOGETHER are NOT sufficient.



I have the solution and the explanation for the question above but I am not entirely convinced of the explanation.

The solution indicates that those 1- top-scoring recruits make up the top 2% (I agree) of the class as a whole – and since the scores are normally distributed, the top 2% represents the third standard deviation above the mean (this is the bit I do not agree with). The top 0.3% represents the third standard deviation above the mean. The top 2% mark is somewhere in between the second and third standard deviation above the mean. Is it still acceptable to approximate “upwards” to the third standard deviation? Forgive my ignorance if this an acceptable assumption. Any input would be much appreciated. Thank you in advance.


Regards,

Pranav

[Alejandro]

which one is the answer the book propose?

[pranavc]

The answer is C.

[mim3]

I think that their explanation is unnecessarily complicated. I got to C a different way (I think):

1. 500 recruits.
We know that the 500 recruits are normally (evenly) distributed across the range of scores with a mean of 72... but we don't know what the range is, so we can't say what the 16th percentile is/how many recruits are below. Insufficient.

2. 10 recruits scored 82 or higher.
Without knowing how many recruits we have we don't know what percentage the 10 recruits represent. Insufficent.

Together, we know that there are 500 recruits and that 10 of them (98th percentile) scored 82 or higher. So, 82 represents the 98th percentile. You can do the computation to find out how many troops fell below the 16th percentile, but you don't have to. Because we know we can, 1&2 together are sufficient and the answer is C.

[chidcguy]

Together, we know that there are 500 recruits and that 10 of them (98th percentile) scored 82 or higher. So, 82 represents the 98th percentile.

I agree until here that 10 members scored in the top 98th percentile and to score in top 98 percentile, one has to score >= 82

You can do the computation to find out how many troops fell below the 16th percentile, but you don't have to. Because we know we can, 1&2 together are sufficient and the answer is C.

I don't understand how we can say that if we know 98th percentile score, we can tell what is the 16th percentile score?

Are you saying that if 82 is the score for 98th percentile, (16/98)X82 is the score for the 16th percentile? Can you this with percentiles?

[akshatsingh]

This question can certainly clear the concepts of normalisation.

Experts please solve to explain the actual answer and not just to answer the 'data sufficiency'.

Help would be really appreciated.

Thanks in advance.

[netigen]

Table to know in this case

range % distribution
1SD 68.26895
2SD 95.44997
3SD 99.73002
4SD 99.99366
5SD 99.99994

this means the you need to find out the SD to solve this problem. If you know the SD you know that the answer will be between 2SD to 3SD below the average

[akshatsingh]

sorry, but this still doesnt help me much..

Is this a standard table ? or a derived one for this problem ?

[pranavc]

I agree about the answer being between 2 and three standard deviations below the mean but doesn't a data sufficiency question try and ask us if we can determine a finite answer as opposed to a range? I am still struggling with the bit about 82 being rounded up to the 98th percentile. Any input would be much appreciated. Thanks in advance.

Pranav