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# The average (arithmetic mean) of a normal distribution of a

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The average (arithmetic mean) of a normal distribution of a [#permalink]

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16 Aug 2010, 10:25
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The average (arithmetic mean) of a normal distribution of a school's test scores is 65, and standard deviation of the distribution is 6.5. A student scoring a 78 on the exam is in what percentile of the school?

A. 63rd
B. 68th
C. 84th
D. 96th
E. 98th
[Reveal] Spoiler: OA

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16 Aug 2010, 10:50
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aiming4mba wrote:
The average (arithmetic mean) of a normal distribution of a school's test scores is 65, and standard deviation of the distribution is 6.5. A student scoring a 78 on the exam is in what percentile of the school?

a.63rd
b.68th
c.84th
d.96th
e.98th

You can solve this question if you know the 68.2-95.4-99.7 rule of normal distributions (though the normal distribution is an absolutely continuous probability distribution and this is not the case in the question): 78 is 2 SD from the mean (65+2*6.5=78), so below it are $$95.4+\frac{100-95.4}{2}=97.7\approx{98}$$ percent of data points, answer E. But don't worry about this question, normal distribution IS NOT tested on GMAT and you don't have to know this rule.
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06 Feb 2011, 19:32
The average (arithmetic mean) of a normal distribution of a school's test scores is 65, and standard deviation of the distribution is 6.5. A student scoring a 78 on the exam is in what percentile of the school?

A
63rd percentile
B
68th percentile
C
84th percentile
D
96th percentile
E
98th percentile
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18 May 2011, 22:33
50 + 34 + 14 = 98%

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19 May 2011, 20:17
50 + 34 + 14 = 98 hence E
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Re: The average (arithmetic mean) of a normal distribution of a [#permalink]

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07 Dec 2012, 10:57
Bunuel wrote:
But don't worry about this question, normal distribution IS NOT tested on GMAT and you don't have to know this rule.

Bueuel,
so they will not test on such problems in GMAT?

also how did you arrive at the answer? more hand holding please.
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Re: The average (arithmetic mean) of a normal distribution of a [#permalink]

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07 Dec 2012, 12:19
Unfortunately or not, i have seen this question on Grockit. Its strange they are throwing such questions that do not have possibilities of being tested on the actual test.
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Re: The average (arithmetic mean) of a normal distribution of a [#permalink]

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08 Dec 2012, 05:06
Simba2012 wrote:
Bunuel wrote:
But don't worry about this question, normal distribution IS NOT tested on GMAT and you don't have to know this rule.

Bueuel,
so they will not test on such problems in GMAT?

also how did you arrive at the answer? more hand holding please.

Yes, normal distribution (and its 68.2-95.4-99.7 rule) is not tested on the GMAT.
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The average (arithmetic mean) of a normal distribution of a [#permalink]

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04 Jun 2013, 09:52
The average (arithmetic mean) of a normal distribution of a school's test scores is 65, and standard deviation of the distribution is 6.5. A student scoring a 78 on the exam is in what percentile of the school?
A)63th percentile
B)68th percentile
C)84th percentile
D)96th percentile
E)98th percentile
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Re: The average (arithmetic mean) of a normal distribution of a [#permalink]

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04 Jun 2013, 12:26
Stiv wrote:
The average (arithmetic mean) of a normal distribution of a school's test scores is 65, and standard deviation of the distribution is 6.5. A student scoring a 78 on the exam is in what percentile of the school?
A)63th percentile
B)68th percentile
C)84th percentile
D)96th percentile
E)98th percentile

E...since the distribution of the curve is 2%,14%,34%,34%,14%,2%
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Re: The average (arithmetic mean) of a normal distribution of a [#permalink]

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04 Jun 2013, 14:16
Stiv wrote:
The average (arithmetic mean) of a normal distribution of a school's test scores is 65, and standard deviation of the distribution is 6.5. A student scoring a 78 on the exam is in what percentile of the school?
A)63th percentile
B)68th percentile
C)84th percentile
D)96th percentile
E)98th percentile

Merging similar topics.
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Re: The average (arithmetic mean) of a normal distribution of a [#permalink]

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04 Jun 2013, 20:48
Stiv wrote:
The average (arithmetic mean) of a normal distribution of a school's test scores is 65, and standard deviation of the distribution is 6.5. A student scoring a 78 on the exam is in what percentile of the school?
A)63th percentile
B)68th percentile
C)84th percentile
D)96th percentile
E)98th percentile

This particular question is out of scope.

Note that mean and SD are tested on the GMAT but normal distributions are not. Then again, a question could mention that scores are normally distributed - the reason for that is that SD concept may not make sense for some distributions e.g. distributions with too much negative skewness etc. Hence they might mention that it is normally distributed for the discerning statistician. Normally, it can just be ignored. Focus only on the SD concepts. e.g. they could ask - which scores are 3 SD away from the mean?
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Re: The average (arithmetic mean) of a normal distribution of a   [#permalink] 04 Jun 2013, 20:48
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