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very challenging problem

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by adam15 » Mon Nov 23, 2009 9:04 pm
the members of the newest recruting 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 arithemtic 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.
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Source: — Data Sufficiency |
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by nikilnikil » Tue Nov 24, 2009 1:44 am
Good question:


In a normal distribution curve, the distribution will be


2% 14% 34% | 34% 14% 2%

The question is asking about the least 16% of population (.. it is asking for 2 Standard deviation less than the mean ). So we have to find the SD.

In total, the question is asking , which information is required to find the Standard deviation?

Given info : Mean = 72

1. 500 students
Not sufficient , we cannot find out anything about wt is the SD.

2. 10 students scored more than 82

Still not sufficient. since we dont know what percent of entire class those 10 students represent.

combining both 1 and 2 ,

We get 10 = x%500
x = 2%. i.e, 82 is 2 standard deviation away from 72 .
2SD = 10
SD = 5
So the SD below which 16% ( 14%+2%) score is 72(mean)- 5 = 67 ,
Sufficient.

Regards,
Nik
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by adam15 » Tue Nov 24, 2009 2:20 pm
Thank you nik for the reply, how did you find the 2%, 14% 34%
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by nikilnikil » Tue Nov 24, 2009 8:31 pm
Hello,

That 2% 14% 34 % ( mean ) 34 % 14% 2% is a standard percentage for normal deviation.

so the curve will be standard on both the sides of a inverted parabola. mean at the center and the parabola is divided into 6 parts.

3 parts towards the left of mean and 3 parts towards right of mean. one part corresponds to 1 SD. Please see the attached pic. you will understand it better.

[/img]
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