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Home values among the 8,000 homeowners of Town X are normall

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GMAT Club Legend
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Joined: 07 Jun 2014
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GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Home values among the 8,000 homeowners of Town X are normall [#permalink] New post 28 Jul 2018, 16:32
Expert's post
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Question Stats:

100% (00:45) correct 0% (00:00) wrong based on 9 sessions
Home values among the 8,000 homeowners of Town X are normally distributed, with a standard deviation of $11,000 and a mean of $90,000.

Quantity A
Quantity B
The number of homeowners in Town X whose home value is greater than $112,000
\(300\)


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: Home values among the 8,000 homeowners of Town X are normall [#permalink] New post 04 Aug 2018, 19:27
90000 + 11000*x = 112000
solving for x; x = 2
The given point is 2SD above mean
Mean is exactly at 50th percentile.
2 SD above mean = 34+13.5 = 47.5 hence number of data % above mean + 2 SD will be 2.5% i.e 2.5/100 * 8000 = 200

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GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4749
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1652 [0], given: 396

CAT Tests
Re: Home values among the 8,000 homeowners of Town X are normall [#permalink] New post 12 Aug 2018, 16:23
Expert's post
Explanation

How many standard deviations above $90,000 is $112,000? The difference between the two numbers is $22,000, which is two times the standard deviation of $11,000. So Quantity A is really the number of home values greater than 2 standard deviations above the mean.

In any normal distribution, roughly 2% will fall more than 2 standard deviations above the mean (this is something to memorize). The value of Quantity A is roughly 8,000 × 0.02 = 160, so Quantity B is greater.
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Re: Home values among the 8,000 homeowners of Town X are normall   [#permalink] 12 Aug 2018, 16:23
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