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Re: A species of insect has an average mass of 5.2 grams and a s [#permalink]
I chose C. I am not very clear with the explanation in support of B. Since 4.9 - 5.5 lies exactly between -1 SD and +1 SD isn't the % of insects with this mass also 34%? So shouldn't the percentages be equal, at least mathematically?
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Re: A species of insect has an average mass of 5.2 grams and a s [#permalink]
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I guess I went with the wrong assumption that within a standard deviation the weights will be equally distributed at each value, so 17% of the weights will lie b/w 4.6 - 4.9 and the other 17% b/w 4.9 - 5.2. Much more clear now, thanks!
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Re: A species of insect has an average mass of 5.2 grams and a s [#permalink]
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A species of insect has an average mass of 5.2 grams and a s [#permalink]
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sandy wrote:
A species of insect has an average mass of 5.2 grams and a standard deviation of 0.6 grams. The mass of the insects follows a normal distribution.

Quantity A
Quantity B
The percent of the insects that have a mass between 5.2 and 5.8 grams
The percent of the insects that have a mass between 4.9 and 5.5 grams


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.


This question is very-very difficult to measure up and answer precisely, if we count on the standard deviation only. Within one standard deviation implies -1 and 1 for any standard normal distribution with the mean equal to 0.

The key to answer correctly on this question, indeed the answer is B, is to begin understanding the central tendency measure concept. One may notice that as the distance goes further from the mean of a distribution, the concentration of data should decrease.

LHS and RHS from the mean we have distance equal, which is equal to the distance or a half of one standard deviation. Nevertheless, the data is more concentrated towards the mean of a distribution.

Note, if we consider only a standard deviation's value and keep moving this distance left- or right-ward, without clearing a central tendency measure, one valid answer coming would be D. But it's not D. LHS and RHS concentration of data exceeds the same for only one side: LHS or RHS.

Correct answer is B.

The central tendency measure is fundamental for understanding and solving GRE standard deviation topic difficult questions.
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Re: A species of insect has an average mass of 5.2 grams and a s [#permalink]
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