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A species of insect has an average mass of 5.2 grams and a s

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A species of insect has an average mass of 5.2 grams and a s [#permalink] New post 28 Jul 2018, 16:28
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Question Stats:

28% (01:15) correct 71% (01:52) wrong based on 14 sessions
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.
[Reveal] Spoiler: OA

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Re: A species of insect has an average mass of 5.2 grams and a s [#permalink] New post 12 Aug 2018, 16:21
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Explanation

Whenever the words “Normal distribution” appear on the GRE, draw a bell-curve diagram that approximates the one below. Memorize the numbers 34 : 14 : 2.

Attachment:
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The middle of the bell curve is the average, or mean, so place 5.2 underneath the 0 in the center; 34%, 14%, and 2% represent the approximate percentages that fall between the standard deviation lines.

For instance, 14% of the population falls between 1 and 2 standard deviations below the mean. Now, use the standard deviation of 0.6 grams to figure out the exact dividing lines between the marked regions of the normal curve. The mass of an insect that is exactly 1 standard deviation above the mean is 5.2 + 0.6 = 5.8, and the mass of one that is 1 standard deviation below the mean is 5.2 – 0.6 = 4.6.

Similarly, the mass at exactly 2 standard deviations above the mean is 6.4 and at 2 below is 4.0.

Attachment:
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Quantity A, the percent between 5.2 and 5.8 grams, is 34%.

However, Quantity B will require some estimating. Note that 4.9 is halfway between 4.6 and 5.2, while 5.5 is halfway between 5.2 and 5.8. Therefore, the area between 4.9 and 5.5, while still a range of 0.6, is under the bigger part of the bell curve in the center. Since the area under the center is bigger than the area between 0 and 1 standard deviations, the percentage of the area under the center must also be greater. Therefore, Quantity B is greater.
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Re: A species of insect has an average mass of 5.2 grams and a s [#permalink] New post 01 Sep 2018, 06:53
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] New post 01 Sep 2018, 10:35
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yashkanoongo wrote:
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?


Not exactly: Notice quantity A is one standard deviation from mean i.e. mean is the lowest value. But quantity B is centered around mean.

Qty is 34.1% where as Qty B is 38.2% to be exact. This is best shown in image below!


Attachment:
Capture.PNG
Capture.PNG [ 28.99 KiB | Viewed 359 times ]

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Re: A species of insect has an average mass of 5.2 grams and a s [#permalink] New post 02 Sep 2018, 01:39
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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!
Re: A species of insect has an average mass of 5.2 grams and a s   [#permalink] 02 Sep 2018, 01:39
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A species of insect has an average mass of 5.2 grams and a s

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