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

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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]  28 Jul 2018, 16:32
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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 _________________ Sandy If you found this post useful, please let me know by pressing the Kudos Button Try our free Online GRE Test Director Joined: 07 Jan 2018 Posts: 604 Followers: 7 Kudos [?]: 546 [0], given: 88 Re: Home values among the 8,000 homeowners of Town X are normall [#permalink] 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 Posted from my mobile device _________________ This is my response to the question and may be incorrect. Feel free to rectify any mistakes GRE Prep Club Legend Joined: 07 Jun 2014 Posts: 4857 GRE 1: Q167 V156 WE: Business Development (Energy and Utilities) Followers: 105 Kudos [?]: 1783 [0], given: 397 Re: Home values among the 8,000 homeowners of Town X are normall [#permalink] 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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Sandy
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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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