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A species of insect has an average mass of 5.2 grams and a s
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28 Jul 2018, 16:28
28 Jul 2018, 16:28
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Question Stats:
46% (01:15) correct
53% (01:44) wrong based on 118 sessions
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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.
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.
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.
Re: A species of insect has an average mass of 5.2 grams and a s
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01 Sep 2018, 10:35
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 [ 28.99 KiB | Viewed 10158 times ]
General Discussion
Re: A species of insect has an average mass of 5.2 grams and a s
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12 Aug 2018, 16:21
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.
Capture.PNG [ 68.26 KiB | Viewed 10239 times ]
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.
Capture.PNG [ 82.33 KiB | Viewed 10231 times ]
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.
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:
Capture.PNG [ 68.26 KiB | Viewed 10239 times ]
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:
Capture.PNG [ 82.33 KiB | Viewed 10231 times ]
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.
