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The lengths of a certain population of earthworms are normal

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GMAT Club Legend
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The lengths of a certain population of earthworms are normal [#permalink] New post 28 Jul 2018, 16:30
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Question Stats:

66% (01:11) correct 33% (00:31) wrong based on 6 sessions
The lengths of a certain population of earthworms are normally distributed with a mean length of 30 centimeters and a standard deviation of 3 centimeters. One of the worms is picked at random.

Quantity A
Quantity B
The probability that the worm is between 24 and 30 centimeters, inclusive
The probability that the worm is between 27 and 33 centimeters, inclusive


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: The lengths of a certain population of earthworms are normal [#permalink] New post 04 Aug 2018, 19:16
Mean = 30
SD = 3
Hence 1 SD below the mean = 27
and 2 SD below the mean = 24
Therefore for normal distribution the% of date at the given range will be 13.5 + 34 = 47.5

While for qtyB the % of data at the given range will be 1 SD above and 1 SD below the mean = 68

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GMAT Club Legend
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Re: The lengths of a certain population of earthworms are normal [#permalink] New post 12 Aug 2018, 16:22
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Explanation

Normal distributions are always centered on and symmetrical around the mean, so the chance that the worm’s length will be within a certain 6-centimeter range (or any specific range) is highest when that range is centered on the mean, which in this case is 30 centimeters.

More specifically, Quantity A equals the area between –2 standard deviations and the mean of the distribution. In a normal distribution, roughly 34 + 34 + 14 + 14 = 96% of the sample will fall within 2 standard deviations above or below the mean. Limit yourself only to the 2 standard deviations below the mean, then half of that, or 96%÷2 = 48%, falls in this range. In contrast, Quantity B equals the area between –1 standard deviation and +1 standard deviation. In a normal distribution, roughly 34 + 34 = 68% of the sample falls within 1 standard deviation above or below the mean. Since 68% is greater than 48%, Quantity B is greater.

Note that exact figures are not required to answer this question! Picture any bell curve—the area under the “hump” (that is, centered around the middle) is bigger! Thus, it has more members of the dataset (in this case, worms) in it.
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Re: The lengths of a certain population of earthworms are normal   [#permalink] 12 Aug 2018, 16:22
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