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 Post subject: GMAT Statistics
PostPosted: Mon May 13, 2013 8:52 am 
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The height of women in Dewaria follows a normal distribution with mean 160 cm and a standard deviation of 6 cm. In a normal distribution, only 0.0063% of the population is not within 4 standard deviations of the mean. If 5 women are more than 184 cm tall, then which of the following is closest to the number of women who live in Dewaria?
A. 16,000
B. 40,000
C. 80,000
D. 100,000
E. 160,000

(E) Since the heights of these women follow a normal distribution, which is symmetric about the mean, there are 5 + 5 = 10 women whose heights are not within 4 standard deviations of the mean. A standard deviation is 6, so 4 standard deviations is 24. There are 5 women below 136 (160 "the mean" minus 24), and 5 above 184 (24 + 160). These 10 women account for 0.0063 % of the total number of women.
So if the number of Dewarian women is n, we can write: n × 6.3 / 100000 = 10, so n = (10/6.3) × 100000 = 160000 approximately. The correct answer is choice (E).
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I am not sure how you calculated 10 women. Could you please explain it more?

Thanks.


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 Post subject: Re: GMAT Statistics
PostPosted: Mon May 13, 2013 8:53 am 
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Joined: Fri Apr 09, 2010 2:11 pm
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The data of women's heights can be presented by the following diagram:
Image

In the normal distribution, only 0.0063% of the population is not within 4 standard deviations of the mean. Those are shown as red points and lie above 184 cm or below 136 cm.

Since any normal distribution is symmetric, then (0.0063/2)% lie above 184 cm (5 pers.) and (0.0063/2)% lie below 136 cm (must be 5 pers. as well). 5+ 5 = 10 .

Note, that 99.9937% of the data are within 4 standard deviations of the mean. Those are shown as blue points and lie between 136 cm and 184 cm.
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