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Home values among the 8,000 homeowners of Town X are normall
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28 Jul 2018, 16:32
28 Jul 2018, 16:32
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Question Stats:
74% (01:06) correct
25% (01:02) wrong based on 63 sessions
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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.
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 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.
Re: Home values among the 8,000 homeowners of Town X are normall
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04 Aug 2018, 19:27
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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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
Re: Home values among the 8,000 homeowners of Town X are normall
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12 Aug 2018, 16:23
12 Aug 2018, 16:23
Expert Reply
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.
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.
