Data Sufficiency

The Members of the newest recruiting class of an organization are taking their physical test and those who score in the bottom 16 % will have to retest. If the scores are distributed normally 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.


Kindly help

dhanda.arun wrote:The Members of the newest recruiting class of an organization are taking their physical test and those who score in the bottom 16 % will have to retest. If the scores are distributed normally 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.


Kindly help

I think the answer is C

I used 68-95-99.8 rule for normal distribution.

mean is 72

Statement I & II clearly alone are insufficient.

Combining I & II

We have to find the SD to find the score.
recruits = 500
10 recruits have scored 82 and higher

1000/500 = 2% of recruits have scored 82 or higher.

2% is 72+3SD = 82 => 3SD=10, SD=10/3=3.33

bottom 16% will have to take the retest

72 - 3.33 = 68.77-72 1st SD 34%
68.66-3.33 = 65.33-68.66 2nd SD 14%
65.33-3.33= 62-65.33 3rd SD 2%

bottom 16% = 68.66 or below

Hence C is the answer.

Why are statements I and II insufficient?

hengirl03 wrote:Why are statements I and II insufficient?

First statement only gives us the no. of recruits. Nothing about below scores or top scores. Insufficient.

Second statement only gives us the top scores and percentage, we dont know anything about sample space i.e. number of recruits.

Hope its clear.

Thanks for the solution.
I still have some doubts:-

1.) what is 68-95-99.8 rule for normal distribution?

2.) How we deduce that 82 is third standard deviation?

dhanda.arun wrote:Thanks for the solution.
I still have some doubts:-

1.) what is 68-95-99.8 rule for normal distribution?

2.) How we deduce that 82 is third standard deviation?

This link will give you a clear idea about the rule.

https://en.wikipedia.org/wiki/68-95-99.7_rule


Also refer to the below post where I have explained in detail about the rule.

https://www.beatthegmat.com/pr-4-standar ... 16015.html

let me know if you still have any doubts.

Thanks dear..
I got it

I agree with the methodology but I think that 82 is 2 standard deviations from the mean (b/c 2% scored higher) not 3 sd's from mean. If it was 3 sd's from the mean, it would have to be 0.1% of the students.